the newtonian scientific revolution, bernard cohen

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The Newtonian Scientific Revolution and Its Intellectual SignificanceAuthor(s): I. Bernard CohenSource: Bulletin of the American Academy of Arts and Sciences, Vol. 41, No. 3 (Dec., 1987),pp. 16-42Published by: American Academy of Arts & SciencesStable URL: http://www.jstor.org/stable/3823825 .

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Stated Meeting ReportThe Newtonian Scientific RevolutionAnd Its Intellectual Significance

I. Bernard CohenWhen the Constitution of the United States

was under discussion, a public dispute arosebetween Benjamin Franklinand John Adams.The dispute centered on the question ofwhether or not there should be a unicameralCongress, consisting merely of a House ofRepresentatives,or a bicameral Congress withboth a House of Representatives and aSenate. The chief point of the argument waswhether the will of the electorate should bedirectly expressed in policy and action accord-ing to its changing moods, as in the case of adirectly elected unicameral legislature. Therewere many who argued for a restrainingforcein the form of a Senate, appointed by thegovernorsand legislaturesof the severalstates.This legislative debate is not my subjecthere. The only aspect that is of concern tome is the form of the argument of JohnAdams, who believed that there should be twohouses of Congress, much as we have today.In his formal presentation Adams argued thatthe bicameral system was the only one thatconformed with Isaac Newton's third law ofmotion, that "to every Action there is alwaysopposed an equal Reaction." In any othercase, he argued, there can be no equilibrium,no rest. It is perhaps of less significance thatJohn Adams didn't correctly understand thesense of the third law of Newton than thathe should have invoked it at all in order tomake a political point. He defended hispreferred form of the constitution by draw-ing on the principles of science established byIsaac Newton.

Who was this man, Isaac Newton? Whatwas the nature of the revolution that heproduced in science? In what sense was the

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revolution so profound that a century laterit figured prominently in political thought?We get some measure of Isaac Newton'sgreatness when we learn that he was theauthor of not only one, but at least two-and maybe even three or four-great revo-lutions. One was in mathematics and theothers in physical sciences. In fact, Newtonmade so many different kinds of fundamen-tal contributions to science that even if wewere to ignore most of them, we would stillhave to rank him as one of the ten or twelvegreatest scientists who ever lived.Isaac Newton was born in 1642, within thevery year of the death of Galileo and onlyabout a quarter of a century after the deathof Shakespeare. He died in 1727, an old manin his eighties, about fifty years before theDeclaration of Independence and the birth ofour nation.Newton was a solitary man, a real "loner."He was born prematurely; his father (also anIsaac Newton) had died shortly before ourNewton was born. He was so small at birth,he later said, that he could be put into a quartmug. His neck was so weak that it was fearedhis head might snap off; they tied him to abolster, head and body, to try to keep himalive.When he was about a year and a half old,his mother remarried and left him in the careof an aged grandmother. He grew up in hisearly years deprived of knowledge of a fatherand without immediate motherly love. Thiswas a terrible time in England: the years ofthe Civil War. Roundhead soldiers cameroughshod into the house because his grand-mother was suspected of royalist tendencies.They threw furniture out of the window andbeat up the servants. It must have been afrightening life for a young lad with nofriends, with no one truly to love him.When Newton was sent to school, he wasat first an indifferent student. He himself hastold an engaging story of how he became ascholar. The occasion was the action of abully in the school who used to beat up on

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him. Young Newton so hated this humiliat-ing physical pain that he practiced until hewas able to take on the bully and fight him.He overcame the bully and was able to rubhis nose in the dirt, as they did then in tokenof victory. But Newton apparently discoveredthat his was only a Pyrrhic victory: the bullywas the number one boy in the school. SoNewton decided he would try to beat him inacademic work, to become a better scholar.Young Newton was absent-minded. Whenhis stepfather died, his mother came back tothe family farm and tried to make a farmerof her son. But his mind was "in the clouds,"and it soon became all too evident that hecould never be successfulat practical farming.One story, told by a neighbor, relates thatyoung Newton, perhaps a lad of sixteen orso, was once asked to lead a horse to mar-ket. When he got there the neighbor askedhim why he was walking along with a halterin his hand. Newton looked around and sawthere was no horse attached to the halter.Newton's family became aware that hewouldn't make a successful farmer. Theydecided that the only thing to do with some-one so far removed from the world of realitywas to send him to the university.They wouldhave him become a preacher. Going to theuniversity was a real step forward;R.S. West-fall has pointed out that so low was the levelof education of Newton's forebears that"before 1642, no Newton in Isaac's branchof the family had been able to sign his ownname." Apparently, according to Newton'scontemporaneous biographer WilliamStukeley, it was the Reverend WilliamAyscough-the brother of Newton's mother,himself a Cambridge man (M.A. 1637) anda Trinity man to boot-who persuaded New-ton's mother to send him to Cambridge andto Trinity.After graduation, Newton stayed on in theuniversity. Many did so in those days. Evi-dently he didn't want to return home; thefarm held no attraction for him. Then thegreat plague swept over England and the

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university was closed. This young man, in hisearly twenties, just barely out of college, wenthome to the family farm. In the course of thenext year and a half, not many years olderthan our college graduates of today, Newtonlaid the foundation for his great career inscience and mathematics. He discovered theprinciples of the differential and integral cal-culus and became one of the greatestmathematicians who ever lived. I belong tothat group of scholars who see in Newton'smathematical work the highest expression ofhis genius. Some measure of his extraordi-nary mathematical prowess may be gainedfrom the fact that in some eighteen to twenty-four months he mastered all of themathematics of his day and began to makehis own great contributions.It was at this time that Newton performedthe renowned series of experiments in opticsthat first brought his name to the attentionof the international world of science. Hemade a hole in a window-shutter, so as toadmit a narrow beam of sunlight into a darkroom. When he caused the light to passthrough a triangular glass prism, he observedthe way in which the sunlight is broken upinto a continuous band of colors, which iscalled a continuous spectrum. Newton soonadvanced far beyond the mere production ofa colored spectrum. He began to wonderwhat causes the sunlight to change into lightof so many different colors. Is it the effect ofthe prism? That is, does the prism "produce"the colors? Or are the colors in the light?Newton came to conceive of sunlight (orany incandescent light) as a mixture of lightof all colors, or-as he put it-a mixture ofall kinds of color-producinglights. The refrac-tion (or the bending of the light) by theprism, or the changing of the direction of thepath of light, as he found by careful meas-urement, is of a different amount for each ofthe colors in the mixture. Each color has itsown unique degree of bending or refractionas it goes from air into glass. Newton con-ceived that the prism produces the spectrum

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by separating the component colors that aremixed in sunlight, a separation that is causedby the differential bending of the colors thatmake up sunlight.Newton relates that it occurred to him thatthere could be an "experimentum crucis," anexperiment of the crossroads, to test his con-ception. That is, he devised an experimentwhich might tell him whether the logical pathhe had picked was the right one, whether histheory was right or wrong.In this "experimentum crucis," he let aspectrum be formed. Then he took a boardwith a hole (or aperture) cut in it so that hecould select from the spectrum a beam oflight of only one color, say green or orange.He then passed this single-colored lightthrough a second prism in order to see whatwould happen. If it was the action of theprism that produced the colors in the spec-trum, then the second prism would cause aspectrum to be formed from the green light.But if the prism merely bent the light, as hehad theorized, then the green light would bebent (refracted)but would remain pure green.When Newton performed this experiment,he found that the green light was bent by thesecond prism and that the light did indeedstay pure green. He tried the same experi-ment for orange and blue, for each of thecolors. In every case the single-colored(monochromatic) light was bent (refracted)bythe second prism, but its color was unaltered.Furthermore, his measurements withmonochromatic light showed that the amountof bending was different for each color, aresult consistent with his guess that the prismseparates the colored lights in sunlight by aprocess of differential refraction.

In this way Newton proved that the actionof the prism is merely to bend the light orrefract it, that the bending is different foreach of the colors, and that sunlight is a mix-true of light of all colors. This was aphenomenal discovery. Newton's discoverytells us the reason why red garments appearto be red when illuminated by sunlight or by20




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the light of an incandescent bulb. The sunand such electric lights give out light of allcolors, but the pigment (the dye in the cloth)absorbs all the colors except red, which itreflects and sends back to our eyes. If we illu-minated those same red garments with bluelight, they would look murky brown or black-ish. Gold leaf looks golden because it reflectsthe part of the sunlight or incandescent lightwhich is yellow and absorbs or transmits theother colors.Newton's discoveries concerning light andcolor were published in the Philosophicalrans-actions f the Royal Society in 1672. This land-mark paper has claim to many "firsts."It wasthe first published paper by Isaac Newton; itwas the first announcement of the moderntheory of color; it was the first major scien-tific discovery to be presented in an articlein a scientificjournal-setting the pattern forscience for all the years to come. Thematerials in this communication were embod-ied in the beginning of Newton's Optickspub-lished in London many decades later, in1704). The Optickscontained much more:experimental studies and analyses of a vari-ety of phenomena which we would classifyunder the rubric of diffraction, including thecelebrated phenomenon we know by thename of Newton's rings. The first editionconcluded with a set of sixteen Queries, anumber increased to twenty-threein the Latinedition of 1704 and increased further tothirty-one in the second English edition of1717/18-Queries which came to embrace notmerely optical problems but the structureandproperties of matter, chemical reactions andthe composition of bodies, the nature of radi-ant heat, electrical phenomena, the cause andmode of operation of the force of gravity, themethods of proceeding in natural philosophy,and even questions of morals. Whereas thePrincipiawas written in Latin in an austeremathematical style, the Opticksappeared inEnglish and was a delight to read. Smallwonder that it engendered a scientific tradi-tion different from that of the Principia.

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Above all, Newton's discoveries about lightwere esteemed because of their paradigmaticvalue in showing the optimal way in whichthe phenomena of nature can be explored byscience. Newton's optical discoveriesprovideda brilliant example of experimental inquiry:the new mode of studying the phenomena ofnature. The pioneers in this new way of doingscience were Galileo, Harvey, Boyle, andNewton himself. As a result of their work,experimental inquiry became recognized asthe key to a great scientific revolution. Thisnew way to discover knowledge was not con-fined to direct experiments, however, since itwas recognized that some subjects could bestudied only by making critical observations.Newton's experimental disciples came toinclude Benjamin Franklin and Antoine-Laurent Lavoisier, the founder of modernchemistry.Newton's discovery of the nature of lightand color was hailed as being particularly sig-nificant because it didn't use complicated,complex, or expensive apparatus, but reliedupon a simple device-a prism-and thecreative imagination of a single individual.

Newton's experimental career illustrates amajor facet of the scientific revolution.Knowledge is to be based upon the senses:on what any man or woman can see or hearor touch or smell, on what can be learnedby experiment and critical observation.Science progresses by direct interrogation ofnature and not on the statements of learnedauthorities.The doctrine that sound knowledge ofnature should be based only on nature andthe exercise of man's reason carried the impli-cation that what mattered in the search forknowledge was how to use one's mind, thatis, to know and to use the correct method.The establishment of the new experiment-based science was a stunning victory for theintellect, a great force of democratization,dealing a death-blow to hierarchy. Now amere youth could perform experiments that

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could either confound or confute the opinionsof his or her elders or confirm the truths ofnature. Pupils skilled in the method of sciencecould now speak with as much authority asteachers and great "masters" had done informer times. What revolution could havebeen greater?Newton was part of this great revolution.

But he recognized additionally that signifi-cant scientific discoveries should be of use.Thus he made a very practical application ofhis findings about light and color and theoptical properties of prisms. To understandNewton's procedure, consider the action ofa lens. We may think of a lens (thick at thecenter and thin at the edges) as if it were apair of prisms base-to-base. Each prism oreach half of the lens acts to produce a spec-trum; therefore, an image produced by a lenshas colored fringes, a phenomenon we callchromatic aberration. Because this chromaticaberration makes the image fuzzy, Newtonsought a way to improve telescopes that wouldnot use lenses. He devised a reflecting tele-scope, using a magnifying mirror. He did notenvisage the possibility that a combination oflenses made of different glass might producean image free of chromatic aberration.Newton actually constructed a small tele-scope of this kind, which was taken fromCambridge to London, where it was demon-strated to the Royal Society. The Fellows ofthe Society (as the members were called)applauded Newton's invention, and theyelected Newton a Fellow of the Royal Soci-ety. When he wrote to thank them, he askedwhen the Society would meet. He wanted tosend them his account of the discovery whichinspired the telescope and which he called"the oddest if not the most considerabledetection which hath hitherto been made inthe operations of nature." The account of hisexperiments and of the conclusions he drewfrom them were published in the journal ofthe Royal Society. Newton waited for theapplause of his fellow-scientists.But scientists,

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like other people, tend often to be jealous andsmall-minded. The letters that were sent into the editor did not commend Newton forhis ingenious experiments and conclusions;rather, they introduced objections about onepoint or another. Newton patiently answeredeach one. Eventually, this arguing became sotedious that Newton resolved he would neveragain publish his discoveries,in order to avoidarguments of this kind. "Philosophy" (orscience), he wrote, is "such an impertinentlylitigious lady," one who invites or demandsarguments or quarrels, that it would be bet-ter to let his discoveries come out after hisdeath than to have to spend the days of hislife defending them.And so Newton became a confirmed kindof recluse in the university. In his early daysas a Fellow of Trinity, he was aware thatwithin seven years, if he wished to continueon the staff as a Fellow,he would be requiredto take holy orders in the Anglican Church.Could he do so in all conscience? To find outhe undertook what was to become a lifelongstudy of religion and theology. He was soonconvinced that he wasn't a strict Trinitarian;he was more like what we would call todaya Unitarian. He couldn't in conscience beordained. The regulations wouldn't allow himto remain a Fellow unless ordained. But hedid stay on in the university. He becameLucasian professor of mathematics whenIsaac Barrow, his predecessor in that chair,resigned it in favor of the brilliant youngerman; now, probably through Isaac Barrow'sinfluence, the Lucasian professorwas granteda special royal dispensation by which he waspermitted to keep his fellowship without tak-ing holy orders. Newton was at liberty to con-tinue his solitary intellectual work.

As a professor, Newton lectured on vari-ous topics in mathematics, on optics, ondynamics, and on celestial mechanics. He alsoworked on problems of chronology. Newtondevised methods, for example, of datingevents of the past by trying to find astronom-24




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ical allusions and then using his knowledgeof precession to discover when these particu-lar heavenly appearances would haveoccurred. In particular,he became concernedwith church history and with comparative orsynchronized chronologies of ancientkingdoms.Another topic of concern to Newton dur-ing these years was the "corruption" of Scrip-ture. He attempted to find out which partsof Holy Writ were the ancient or originaltexts and which were later accretions oremendations and sought for "scientific" stan-dards by means of which to distinguish thetwo. Newton also studied and wrote aboutchurch history. Much of his intellectual effortwas expended on a study of the propheticbooks of the Bible: the Book of Daniel andthe Book of Revelation.He believed there was a secret language ofprophecy. If only he could find out the keyto that language, he would understand theprophecy he assumed God must have con-cealed in the text of Holy Writ. Newton wasfully convinced that in this way he could finda key to the ultimate fate, purpose, or des-tiny of the universe. Newton's deep concernwith prophecy remained an abiding passionof his intellectual life.Newton was deeply interested in problemsof matter, which led him to the topics ofalchemy and chemistry. He spent many hoursof study and experiment on alchemy.Alchemy was a subject whose main concernwas to master the properties of matter socompletely and deeply as ultimately to gainthe ability or power to transmute one elementinto another. In Newton's day, many peoplebelieved matter to be made up of primordialor ultimate particles. Hence if a scientistcould find a way to break into these primor-dial components and then recombine them,he should be able to change one kind of mat-ter into another. We know today, of course,that the methods explored by Newton, Boyle,Locke, and other students of alchemy couldnot ever have produced the desired transfor-

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mation. Yet we are all too aware today thatsuch transmutations are in fact possible. Weproduce them in our laboratories regularly.Who does not know that by radioactive dis-integration nature is busy transmuting onechemical element into another all the time?We are not surprisedto find that Newton wasno ordinary student of alchemy; unlike theothers, he attempted to introduce precisionand quantitative considerations into alchem-ical theory, so as to make this subject ulti-mately an exact science like astronomy andphysics.During the years of Newton's tenure of the

Lucasian professorship, many men of sciencewere concerned about the physics of theuniverse. A main research task was to findout what kind of force or forces-if any-may hold our solar system together. Whatkind of force must there be to keep theplanets moving in orbit around the sun?What keeps moons or satellites moving inorbits around their respective planets as inthe case of Saturn, the earth, or Jupiter?These questions were at the center of ascientific correspondence that began in 1679between Robert Hooke in London and IsaacNewton in Cambridge. Hooke was one ofthose who had earlier most stronglychallenged Newton's theory of light. Now, hehad just been appointed Secretary of theRoyal Society. He wrote to Newton saying,in effect, let bygones be bygones. Let us, hesuggested, explore questions of sciencetogether.During their exchange of letters, Hooketaught Newton what was for him a new prin-ciple for analyzing motion. Newton knew thatif a body could move freely, without anyresistance or without any force acting on it,it would tend to go off in a straight line.That's the principle of inertia. Newton hadlearned this principle from reading Descartes.When a body moves in orbit, however, itdoesn't fly off in a straight line; it constantlyfalls in toward the center. We would say that

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the body stays on the curve because the rateof falling is of just such a magnitude that thefalling away from a tangential inertial pathand consequent descent toward a center keepsit on the curve. If it fell any faster it wouldget inside its curved orbit and spiral closerand closer to the center. Conversely, if it fellmore slowly, it would spiral out in an everincreasing orbit. Hooke made it clear to New-ton that the way to study a planet's orbit isto break up the motion into two parts. Oneis the linear inertial motion, out along a tan-gent to the curve; the other is an acceleratedmotion of falling inward toward the sun.Newton himself had not hit upon this modeof analysis; presumably he had been ledastray by concentrating on the misleadingconcept of "centrifugal" force. Hooke,however, despite the brilliance of his physico-mathematical intuition, was not sufficientlyskilled in mathematics to carry out the con-sequences of his own ideas.There can be no doubt that Newton wasvery much impressed by Hooke's mode ofanalysis. In one of his letters, he freely con-fessed to Hooke that he had not ever heardof it until then. In his own private papers,Newton began to work out the consequencesof what he had learned from Hooke. Beforelong he discovered that Kepler's law of areasfor the planets had the physical significancethat there must be a force directed toward thesun, a force that regulates but does not causethe motions of each of the planets. There isa similar force directed toward each planetthat regulates the motion of its satellites.Before long, Newton found the physicalmeaning of the law of elliptical orbits, alsodiscovered by Kepler. This law, Newton dis-covered, implies that the force in questionvaries inversely (or reciprocally)as the squareof the distance.When we say that the force varies inverselyas the square of the distance, we mean thatif the distance is doubled, the force is not one-half of the original but one-quarter (one overtwo-times-two or one over two-squared). If we

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triple the distance, go to a point three timesas far away, the force is not a third but aninth.Once having found his law of force,Newton-being secretive by nature and hav-ing evidently been hurt by that earliercontroversy-told no one about his great dis-covery. Then in 1684, about four years later,the veil of secrecy was broken.It happened that at the Royal Society ofLondon, the leading scientific society of theworld, there was great concern about thequestion of elliptical orbits and the law ofareas. Three who were particularly exercised

about the question were the astronomerEdmond Halley, famous for the comet namedafter him; Christopher Wren, the celebratedarchitect, who was also a geometer and phys-icist, an astronomer, and a pioneer in bio-logical experimentation; and Robert Hooke.None of the three saw how to solve theproblem. Then Halley thought of the greatmathematician in Cambridge. Surely, if any-one could solve this problem, Newton wouldbe the one. He decided he would pay New-ton a visit to see if he could get him to workon the law of force. We have a record of hissubsequent conversation with Newton. Heapparently asked Newton what the orbit ofplanets would be under an inverse-squarelawof force. Newton replied, "An ellipse." WhenHalley then asked Newton how he knew this,Newton is recorded as having replied, "I havecalculated it."

Halley, quite naturally, asked Newtonwhether he might see the calculations. ButNewton couldn't find them. He promised,however, that he would keep on looking. Inthe end he had to reconstruct his work. Even-tually he wrote up his results and sent themto Halley in London.Halley was so impressed that he rushedback to Cambridge. He told Newton howimportant this work was. He begged Newtonto write up his work more fully so that itcould be recorded at the Royal Society. He

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wanted Newton to have proof of his priorityin the great discovery.Newton did just that. As he began to workon the problem, he was led from one topicto another. Eventually, he developed his ideasfully into a book. In this creative process, healtered his original concepts and made oneof the greatest creative leaps forward everrecorded in the history of science. Let me tryto present Newton's bold invention as sim-ply as possible.Newton had been studying the force withwhich the sun pulls on the earth, or any otherplanet, so as to make it keep falling. The

result of the action of such a force is that eachplanet moves in a curved orbit around the sunrather than flying off in a straight line. Even-tually, it occurred to Newton that if the sunpulls on the earth, then-according to the lawof action and reaction, which we haveencountered in relation to John Adams andthe Constitution-the earth must also pull onthe sun. The same would be true for the sunand Mars or Jupiter or any of the planets.Each of the planets is pulled on by thesun;hence, by the law of action and reaction, eachin turn pulls on thesun. This means that eachplanet, say earth or Mars, is both a centeror activator of the pulling force and a bodyon which the pulling force acts. If each planethas that dual role, then each planet must bothpull on all the other planets and be pulledby all of them. Newton concluded that it isn'tjust the sun that pulls on the planets; theplanets also pull on one another.This conclusion, which Newton reached inlate 1684, was astonishing. Newton wonderedif it was true. Fortunately, an experimentaltest was possible. In those years, the planetSaturn was moving in orbit rather near theplanet Jupiter. Jupiter is the most massiveplanet in the solar system; its mass is greaterthan that of all the other planets addedtogether. The second most massive planet isSaturn. It occurred to Newton that if Jupiterdoes pull on Saturn, there ought to be some

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observable evidence of the slowing down ofSaturn after it passes by Jupiter. AccordinglyNewton wrote a letter to the "AstronomerRoyal," John Flamsteed, for information ona possible alteration of Saturn's motion as aneffect of Jupiter's action. Flamsteed foundthat this change was indeed discernible andwas of the order of magnitude that would beexpected from Newton's imaginative con-clusion.A stage in reasoning about this pullingforce is to shift attention from planets to theirmoons. If the earth and the planets pull onone another, or are activators of the pullingforce, then the earth and the planets must alsopull on their respective moons. Newton usedthis conclusion in a boldly imagined test tosee if the earth does indeed have such a pull-ing power. Is this pulling power the same as"gravity," the force that on earth is the causeof common weight?

His test made use of the well-known factthat on the earth's surface (one earth-radiusfrom the earth's center) a freely falling bodyhas a downward acceleration of very nearly32 feet per second in every second. Heimagined a "test body" to be placed in spaceat a distance of 60 earth-radii from the earth'scenter. Supposing that the earth's gravityextended out to 60 earth-radii, what wouldbe the body's rate of fall toward the earth?We have seen that Newton had shown thatthis force would vary inversely as the squareof the distance. The word "inversely" in thiscontext means that the "power" or effect ofthe force decreases as the distance increases.The expression "inversely as the square"quantifies this decrease. In accordance withour earlier explanation, if we know the forceat the earth's surface (one earth-radius fromthe earth's center), then at two earth-radiifrom the center, the distance would be dou-bled (multiplied by two), so that the forcewould now be one-quarter of what it was(1/4th, since 4 is the "square" of 2). At threetimes the distance, the force is but one-ninthof the original (1/9th, since 9 is the square

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of 3). And so, out at 60 earth-radii from theearth's center, the force would be not 1/60th,but 1/3600th of 32 feet per second in eachsecond. On the basis of the theory we canthus easily calculate how far toward the eartha body would fall in one second of time ifit were placed at a distance of 60 earth-radiifrom the earth's center.Newton, of course, was fully aware thatthere actually is a body in space, out at 60earth-radii from the earth's center. It is ourmoon. We know exactly how quickly themoon moves in its orbit, and it is a relativelysimple matter to compute how fast it falls.In solving this Newtonian problem, using the

method of analysis of orbital motion whichNewton learned from Robert Hooke in1679/80, one finds that the moon falls con-stantly toward the earth while moving for-ward; the rate of fall is just the right amountso that the moon keeps "falling" to thecurved lunar orbit. The Newtonian calcula-tions show that the predicted value of fall forthe moon lies within 1/10th of one percent ofthe observed value.Newton's test shows that gravity, this pull-ing force of the earth-whatever it is thatproduces weight, heaviness, or "gravitas" (inLatin)-extends out as far as the moon. Thisgravity must vary as the inverse square of thedistance. Newton was a sound philosopher;he concluded that the force he had found tobe acting between the earth and its moonshould be the same force (or a force of thesame sort) that acts between Jupiter and itsfour moons. It is also the same force that actsbetween the sun and the planets. This con-clusion is in accord with Newton's "Regu-lae Philosophandi," or Rules of Proceedingin Natural Philosophy: that one should notpropose more causes of natural phenomenathan are necessary; that to the same naturalphenomena we should-as far as possible-assign the same cause. This kind of reason-ing led Newton to conclude that terrestrialgravity extends from the earth to the moon;it is this same force of gravity that acts

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between Jupiter and its moons and betweenthe sun and planets. This is Newton's firststage in showing that the pulling force whichwe know on earth as gravity is universal.By mathematics, inductive logic, and atremendous intellectual leap of the imagina-tion, Newton was able to extend the argu-ment to any two bodies, wherever they maybe in the universe. He announced that anypair of such bodies will "attract" each otherwith this force of universal gravity. It is thisconcept of a force of universal gravity whichis the central idea in Newton's great book.It is this force of universal gravity which holdsthe universe together and regulates themotions of its parts.Newton gave his famous treatise the titlePhilosophiaeNaturalisPrincipiaMathematica, r"Mathematical Principles of NaturalPhilosophy."This book was published in Lon-don in 1687, just three centuries ago. It is inthis work that Newton sets forth the moderndefinition of mass. It is in the Principiahathe explores the actions of forces and enunci-ates the three laws of motion. Here he setsforth the general principles of universalgravity and its quantitative expression or law.And it is in the Principiahat Newton applieshis studies of dynamics to the system of theworld, showing that the universe is heldtogether and performs the motions of its partsaccording to the principle of universal gravity.

In order to give you some idea of howrevolutionary the Newtonian principles were,let me mention some of the new explanationsof natural phenomena that Newton produced.First of all, it had become known in New-ton's day that for a pendulum clock to keepcorrect time as it is moved from one latitudeof the earth to another, the length of the pen-dulum must be constantly changed. As wewould say today, following Newton, the sur-face force of the earth's gravity changes withlatitude. Newton explained this observedphenomenon in terms of the effect that therotation of the earth and the earth's shape

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have on the force of gravity.The shape of theearth, according to Newton, is an oblatespheroid, a "squashed" sphere that has beenflattened at the poles and bulges at theequator.It is an additional consequence of thisshape, he demonstrated, that the gravitationalaction of the moon on the rotating earth mustproduce what is called precession, a rotaryturning motion of the axis of the earth. Thisphenomenon of the precession of the earth'saxis had been known to astronomerssince thesecond century B.C., when it had been dis-covered by Hipparchus. But no one beforeNewton had reduced this phenomenon ofprecession to its physical cause. Newton'swork aroused great admiration because, withpencil and paper and mathematics, he hadbeen able to compute the actual shape of theearth.One of Newton's most spectacular achieve-ments was to show how the tides in the oceansand seas result from the combined gravita-tional attractions of the sun and moon on thewaters. Kepler had suspected that some"influence" of the moon might be involvedin the phenomena of tides in the oceans, butmost scientists agreed with Galileo that thisfantasy was "unscientific." So it came assomething of a surprise that Newton set fortha demonstration that tides are caused by thegravitational pull of sun and moon.After the Principia ad been published, andespecially after the revised edition of 1713,Newton was particularly celebrated for hisgravitational explanation of the motions of themoon. Newton showed how the irregularitiesin the moon's motion were produced througha combination of the gravitational action ofthe sun and of the earth. The earth and moonform a gravitating pair, each moving in orbitabout their mutual center of gravity, but per-turbed by the sun's gravitational attraction.By this analysis Newton shifted the study ofthe moon's motion from a problem in celes-tial geometry and pure curve-fitting to aresearch program based on physical causes.

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Newton himself was not able to completethe study of the earth-moon-sun system, thefamous "three-body problem," but he setastronomers on a wholly new direction ofresearch and practice-a sign of the revolu-tionary quality of his innovation. Newton'sprogram for studying the moon's motions inrelation to causes was one of practical andnot mere theoretical importance. In Newton'sday it was generally understood that the abil-ity to predict future positions of the mooncould be of significant help in solving thepressing problem of finding longitude at sea.Newton's complete reorientation of lunarresearch was recognized by readers of thePrincipiaas an unexpected breakthrough. Ina review of the second edition of the Principiain the most important journal of those days,the Acta Eruditorum,he reviewer especiallycommended Newton for this achievement."The computation Newton has made of themotions of the moon from their own causesthrough the theory of gravity," he wrote,"proves the divine force of intellect and out-standing sagacity of the discoverer."In each of the foregoing examples-theorbital motion of planets and their moons,the variation of weight with terrestrial lati-tude, the oblate shape of the earth and theprecession of the earth's axis, the cause of thetides, and the regularities and variations inthe moon's motion-we may see an outstand-ing feature of the Newtonian system of theworld. In each a group of phenomena isexplained by the action of the force of univer-sal gravity, producing its effects according tothe Newtonian principles of dynamics,expressed in the three laws of motion.In Newton's system of the world, there isone principal or unifying concept, universalgravity, that serves "to explain" the diverseobserved phenomena. In this context, theword "explain" means that Newtonaccurately and successfully predicted andretrodicted the phenomena of the heavens andthe earth. It was a formidable achievement.

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One of the most significant sets ofphenomena studied by Newton was themotion and successively changing appear-ances of comets. Almost half of the third andfinal "book" of the Principiawas devoted tocomets. In order to see why comets have sospecial an importance in the Newtonian sys-tem, let us attempt a reconstruction of New-ton's line of argument. Comets are made ofmatter; that is, they have mass. ThereforeNewton's principles imply that they must besubject to the action of gravity, notably thesun's gravity. In this case, as Newton said,they have to move in orbit as a "kind ofplanet." The consequence of such reasoning,according to the gravitational system set forthin the Principia,must be that some cometsmove in orbits that are large ellipses, with thesun located at a focus. These very largeattenuated elliptical orbits extend out to thefar reaches of space. Comets, Newton thuswas led to conclude, must in some cases comeback regularly to the visible part of our solarsystem after traveling out in space for manyhundreds of millions of miles.In those days comets were thought to besingular or one-time events. Newton came tothe very revolutionary conclusion that manycomets return periodically, at regular inter-vals, moving in closed orbits with the samekind of recurring motion observed in theplanets. Halley improved upon Newton's the-ory in some details, and he searched throughthe records of history to see if he could findregular sequences which could be presumedto be reappearances of one and the samecomet with cyclical regularity. One of thecomets studied by Halley proved to have aperiod of about 75 years. He made the New-tonian prediction that it would reappear inthe 1740's. This was perhaps the first timethat anyone had been willing to submit a newphysical theory to such a daring and dramaticpublic test. Halley made a prediction of amajor event that would not occur for somehalf a century or more. Halley knew, further-more, that if the comet should appear exactly

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as he had predicted, the result would con-tradict the accepted beliefs that scientists andnon-scientists had held for many centuries.Such a successful long-term prediction wouldprove the validity of the Newtonian celestialphysics based on the concept of universalgravity. It is well known that the comet cameback exactly on time: a stunning triumph forHalley's theory and for the Newtonian sys-tem of the world.In the Principia,Newton presented a newphysics and a new system of the world basedon universal gravity. At once a profoundproblem arose: how can a grasping force such

as gravity travel out from the sun overhundreds and hundreds of millions of milesand in some unexplained way be able at sucha distance to affect a planet? This solargravitationalforce must also be able to extenditself even further into the distant reaches ofspace, way beyond our visible range, in orderto be able to act on a comet and cause it toturn around and come back to the visible partof our solar system. Can we really believe thata physical force can travel out through sogreat a distance and still be so powerful asto produce these alleged effects? Technicallythis is the problem of "action-at-a-distance":how can a body (like the sun) act at a dis-tant place where it "is not"?Most of the philosophers and the membersof the scientific community of Newton's daywere deeply troubled by the Newtonian con-cept of universal gravity.Some said that New-ton had taken a retrograde step. Inintroducing the motion of attraction, theyaverred, he had brought back into the dis-course of science the "occult qualities" of abygone age which had supposedly been dis-missed once and for all. Others simplyrejected the Newtonian celestial mechanicsand the Newtonian system of the worldbecause of their open antipathy to the ideaof gravitational attraction. Newton himselfwas troubled. He wrote that no one who heldsound principles of philosophy could possibly

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believe that a body can act "where it is not."At that time the reigning or "received"philosophy of science was based on the ideasof Rene Descartes. Known widely as the"mechanical philosophy,"this system of beliefwas posited on the notion that all physicalexplanations of phenomena must be based ontwo (and only two) principles: matter andmotion. There was no place in this philosophyfor a force acting at a distance. We have seenthat Descartes himself had invented a systemof the world in which the planets were imbed-ded in huge vortices of swirling "aetherealmatter," which caused them to move in orbitaround the sun. In the Principia,Newtonshowed that this particular Cartesian systemof cosmology must be false since it leads toconclusions that are inconsistent with Kepler'slaws. Since Newton adhered more or less tothe principles of the mechanical philosophy,he was faced with a real dilemma! He hadshown how a force of universal gravity canaccount for the observed phenomena of ouruniverse, but how could he believe in a forcethat acts in such a way as to contravene fun-damental philosophical principles?Newton's response was to seek-in vain, asit turned out-to find how this force couldact in a way that would not contradict themechanical philosophy. Many hours ofthought and research were expended on thisquest. At one time, Newton thought thatgravity might be explained by electricity, anew subject in physics being explored in histime. Perhaps, he mused, gravitational forcemight be related to, or caused by, the parti-cles of electrical "effluvia." At another timehe had hopes that some kind of "shower" ofeffluvial particles might force one bodytoward another. He also envisioned thatgravity could be explained by variations inthe density of an all-pervading aether or"aethereal medium." But these attemptstended to founder because of Newton's thirdlaw and its effects: each of two bodies had tobe made to gravitate toward the other andto do so according to the rule of the "inverse

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square of the distance." None of his"mechanical" explanations, whetheraethereal or electrical, could produce a mutu-ally acting force of gravity that would agreewith the quantitative measure of the inversesquare.In the end there was no easy solution forNewton. He would not be satisfied by invent-ing unsupported hypotheses. Newton dis-cussed this problem in a famous concluding"Scholium Generale," which he wrote for thesecond edition of his book (1713). Here hesaid that he would not feign hypotheses inplace of sound scientific explanations:"Hypotheses non fingo," "I do not feignhypotheses." Universal gravity,he said, reallyexists, "revera existit." Furthermore, univer-sal gravity acts according to the inversesquare law of the distance. This force servesto explain "abundantly" the motions of bod-ies on the earth and also the motions ofplanets, of the moon, and of the tides in thesea. That, he said, is enough: "Satis est." Itis enough that this force (which really exists)does explain the phenomena. Newton's con-clusion was that we should accept and use thisforce even if we do not understand it, evenif we cannot explain how it acts. (The word"explain" in this context implies that theaction of gravity must somehow be made toaccord with the principles of the receivedmechanical philosophy.) In short, Newtonargued that his system of celestial mechanicsand his system of the world need not berejected simply because the basic conceptapparently ran counter to the receivedphilosophy. What was more important wasthe proven fact that universal gravity couldexplain so many phenomena. For science,"that is enough."Newton's General Scholium set forth a newview of science: a philosophy of science of thenew order, a new scientific credo. Newton wassaying that the goal of science is not to seekultimate explanations. Rather, the scientistshould found his or her concepts uponexperience; if their use makes it possible to

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accurately predict and retrodict thephenomena of nature, "that is enough."Newton set forth a simpler goal for sciencethan the traditional search for "first causes,"for ultimate explanations. By and large, scien-tists have been following the "Newtonianway" ever since. It is curious that the reso-lution of Newton's failure produced thereorientation of the aim of science.There is a final intellectual question thatarises before we can leave the subject of theNewtonian Revolution. How was it possiblefor this difficult and largely unreadable bookto exert so great an influence as to dominate

thinking-even in the areas of politics andgovernment-for over two centuries? How didsuch a work establish a model for all thesciences and even the social sciences, if it wasdevoted, as its title proclaims, to MathematicalPrinciples f NaturalPhilosophy?Mathematics is a difficult and-for mostreaders-a forbidding subject. Newton's bookis mathematical in the extreme. Therecouldn't have been many people who wereable to read it when it first appeared.Newton said that he had purposely made

his Principia ifficult to read, evidently in thehope that smatterers (who would not be ableto follow the mathematics) would not be ableto criticize the doctrine of universal gravityon purely philosophical or ideologicalgrounds.With so small an anticipated readership,the original edition was small, limited to somethree hundred or perhaps at most threehundred and fifty copies. How then did itproduce its effect? The answer to this ques-tion is of interest to all students of intellec-tual and cultural history. The influence of thePrincipiaarose primarily through the effortsof a series of inspired educators and greatpopularizers.The first person who attempted to explainthe Newtonian principlesto the general publicwas a British clergyman and classicist,Richard Bentley. In the 1690's Bentley gave

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an inaugural series of sermons on a newfoundation, established by the will of RobertBoyle, sometimes known as the "father ofchemistry."Bentley's "Boyle Lectures," as hissermons were called, were devoted to a con-futation of atheism. The last two addressedthis topic from the point of view of "theframe of the world." Bentley gave a succinctexposition of the Newtonian physical princi-ples and then argued that the Newtonian sys-tem of the world must be the best possibleargument against atheism, since (by unim-peachable mathematics) it demonstratesGod's design in the universe. Bentley was noscientist, but Newton himself was Bentley'sadvisor on how to study the Principia.OtherBoyle Lectures in succeeding years introducedvariations on the same Newtonian theme.Since the lectures were reprinted again andagain, many readers became familiar withNewtonian principles and the Newtonian sys-tem of the world through these publishedsermons.A second set of expositors wrote booksexpressly designed to explain the "Newtonianphilosophy" for non-mathematicians andeven non-scientists. The first was written byHenry Pemberton, a medical doctor and amathematician, who had edited the third edi-tion of the Principia nder Newton's direction.According to Pemberton, Newton had favoredthe design of such a work and had even givenhis approvalto some parts of the book, whichPemberton had read aloud to him. Anothersuch introduction to Newtonian science fornon-scientists was written by Colin Maclau-rin, an outstanding mathematician whosename is well known to anyone who hasstudied the calculus, since the "Maclaurinseries" is named after him. Both of thesebooks are very sound and are still rewardingto read today. They give explanations of theNewtonian principles of science in a way thatmakes it easy for persons without mathemat-ical training to understand. Each of themwent through a number of editions and wastranslated into French.

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Perhaps the best of the books of this kindwas written by the philosopher Voltaire.Often, when I am asked by students or col-leagues to recommend a book that constitutesa sound introduction to Newtonian science,I do not choose a scholarly work of our ownday. Rather, I suggest Voltaire's ElementsfSirIsaac Newton's Philosophy,written almost twohundred and fifty years ago. This work wasrated so highly that it was rapidly translatedinto English. Men and women of Newton'sown nation were thus educated in the prin-ciples of Newtonian science by a foreigner.Voltaire had learned his Newtonian physicsand celestial mechanics with assistance froman able mathematician and physicist, theMarquise du Chastellet. The "divine Emily"wrote her own study of Newtonian science.Even more important, she produced a Frenchtranslation, published with a commentary in1756/1759, of the whole of Newton's Principia.The "editor" supplied an introduction com-mending this translation, which he declaredto be far superior to the English translationby Andrew Motte (1729). It is even betterthan Newton's own Latin text, he declared,because the Marquise had clarified certainpassages where Newton's own text was uncer-tain. Voltaire added, in his "historicalpreface" to the translation: "We have seentwo wonders: one, that this work has beencomposed by Newton; the other, that it hasbeen translated and clarified by a woman."

In the Age of the Enlightenment, it wasgenerally agreed that the Newtonianphilosophy should be known and understoodby everyone. There were books written tohelp people understand Newtonianism atalmost every level of readership.One of them,written in Italian by Francesco Algarotti, wascalled II Newtonianismoper le dame,or Newtonian-ismfor theLadies. t was translated into Englishand was reprinted again and again. In thosedays ladies presumably didn't commonly havethe advantage of formal education and couldnot read Newton directly. But Algarottiproved they too could learn the principles of

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the Newtonian philosophy.Some other expositors conceived that theNewtonian principles could most easily betaught to non-scientists if they were illustratedby experimental demonstrations. WilliamWhiston and J.T. Desaguliers were thepioneers in organizing public lectures onNewtonian science based on experiments. Inall these different ways the principles of New-tonian science and the basis of the Newto-nian philosophy spread to all levels ofthinking men and women.So great was the general admiration forNewton and his achievement that few wouldhave disagreed with the sentiment expressedin that famous couplet written by AlexanderPope:

Nature, and Nature's Laws lay hid in Night.God said, Let Newtonbe! and All was Light.But, as everyone knows, science is bynature cumulative and progressive. There arealways new revolutions and the constantintroduction of radically new scientific ideaswhich negate established thought. Even sofundamental a work as Newton's could notstand forever without any alteration.In our own century, Newton's work hashad to be revised, extended, and rewritten-

primarily by Albert Einstein. We can expresspoetically the new theme of Newton and Ein-stein by adding a couplet of the twentieth cen-tury to the famous eighteenth-century linesof Alexander Pope. The addition by J.C.Squire makes a quatrain for our time.Nature and Nature's laws lay hid in night:God said, 'Let Newton be!' and all was light.It did not last: the Devil howling 'Ho,Let Einstein be,' restored the status quo.

I. Bernard Cohen is VictorS. Thomas ProfessorEmeritusof theHistoryof Scienceat HarvardUniver-sity. His communicationwas presented t the 1678thStatedMeeting, held in Cambridgeon March 11,1987 An expandedversionof this communication illappearas an article n theHarvard Library Bulle-tin, December 1987

the newtonian scientific revolution, bernard cohen

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