Isaac Newton (1642–1727) is best known for having invented thecalculus in the mid to late 1660s (most of a decade before Leibniz didso independently, and ultimately more influentially) and for havingformulated the theory of universal gravity — the latter in hisPrincipia, the single most important work in thetransformation of early modern natural philosophy into modern physicalscience. Yet he also made major discoveries in optics beginning in themid-1660s and reaching across four decades; and during the course ofhis 60 years of intense intellectual activity he put no less effortinto chemical and alchemical research and into theology and biblicalstudies than he put into mathematics and physics. He became a dominantfigure in Britain almost immediately following publication of hisPrincipia in 1687, with the consequence that“Newtonianism” of one form or another had become firmlyrooted there within the first decade of the eighteenth century. Hisinfluence on the continent, however, was delayed by the strongopposition to his theory of gravity expressed by such leading figuresas Christiaan Huygens and Leibniz, both of whom saw the theory asinvoking an occult power of action at a distance in the absence ofNewton's having proposed a contact mechanism by means of which forcesof gravity could act. As the promise of the theory of gravity becameincreasingly substantiated, starting in the late 1730s but especiallyduring the 1740s and 1750s, Newton became an equally dominant figureon the continent, and “Newtonianism,” though perhaps inmore guarded forms, flourished there as well. What physics textbooksnow refer to as “Newtonian mechanics” and “Newtonianscience” consists mostly of results achieved on the continentbetween 1740 and 1800.

• 1. Newton's Life
  • 1.1 Newton's Early Years
  • 1.2 Newton's Years at Cambridge Prior toPrincipia
  • 1.3 Newton's Final Years at Cambridge
  • 1.4 Newton's Years in London and His Final Years
• 2. Newton's Work and Influence
• Bibliography
  • Primary Sources
  • Secondary Sources
• Academic Tools
• Other Internet Resources
• Related Entries

1. Newton's Life

Newton's life naturally divides into four parts: the years before heentered Trinity College, Cambridge in 1661; his years in Cambridgebefore thePrincipia was published in 1687; a period of almosta decade immediately following this publication, marked by the renownit brought him and his increasing disenchantment with Cambridge; andhis final three decades in London, for most of which he was Master ofthe Mint. While he remained intellectually active during hisyears in London, his legendary advances date almost entirely from hisyears in Cambridge. Nevertheless, save for his optical papers ofthe early 1670s and the first edition of thePrincipia, allhis works published before he died fell within his years in London.^[1]

1.1 Newton's Early Years

Newton was born into a Puritan family in Woolsthorpe, a small villagein Linconshire near Grantham, on 25 December 1642 (old calendar), a fewdays short of one year after Galileo died. Isaac's father, afarmer, died two months before Isaac was born. When his motherHannah married the 63 year old Barnabas Smith three years later andmoved to her new husband's residence, Isaac was left behind with hismaternal grandparents. (Isaac learned to read and write from hismaternal grandmother and mother, both of whom, unlike his father, wereliterate.) Hannah returned to Woolsthorpe with three new children in1653, after Smith died. Two years later Isaac went to boardingschool in Grantham, returning full time to manage the farm, not verysuccessfully, in 1659. Hannah's brother, who had received an M.A.from Cambridge, and the headmaster of the Grantham school thenpersuaded his mother that Isaac should prepare for theuniversity. After further schooling at Grantham, he enteredTrinity College in 1661, somewhat older than most of hisclassmates.

These years of Newton's youth were the most turbulent in the history ofEngland. The English Civil War had begun in 1642, King Charleswas beheaded in 1649, Oliver Cromwell ruled as lord protector from 1653until he died in 1658, followed by his son Richard from 1658 to 1659,leading to the restoration of the monarchy under Charles II in1660. How much the political turmoil of these years affectedNewton and his family is unclear, but the effect on Cambridge and otheruniversities was substantial, if only through unshackling them for aperiod from the control of the Anglican Catholic Church. Thereturn of this control with the restoration was a key factor inducingsuch figures as Robert Boyle to turn to Charles II for support for whatin 1660 emerged as the Royal Society of London. The intellectualworld of England at the time Newton matriculated to Cambridge was thusvery different from what it was when he was born.

1.2 Newton's Years at Cambridge Prior toPrincipia

Newton's initial education at Cambridge was classical, focusing(primarily through secondary sources) on Aristotlean rhetoric, logic,ethics, and physics. By 1664, Newton had begun reaching beyond thestandard curriculum, reading, for example, the 1656 Latin edition ofDescartes'sOpera philosophica, which included theMeditations,Discourse on Method, theDioptrics, and thePrinciples of Philosophy. Byearly 1664 he had also begun teaching himself mathematics, takingnotes on works by Oughtred, Viète, Wallis, and Descartes— the latter via van Schooten's Latin translation, withcommentary, of theGéométrie. Newton spent allbut three months from the summer of 1665 until the spring of 1667 athome in Woolsthorpe when the university was closed because of theplague. This period was his so-calledannusmirabilis. During it, he made his initial experimentaldiscoveries in optics and developed (independently of Huygens'streatment of 1659) the mathematical theory of uniform circular motion,in the process noting the relationship between the inverse-square andKepler's rule relating the square of the planetary periods to the cubeof their mean distance from the Sun. Even more impressively, by late1666 he had becomede facto the leading mathematician in theworld, having extended his earlier examination of cutting-edgeproblems into the discovery of the calculus, as presented in his tractof October 1666. He returned to Trinity as a Fellow in 1667, where hecontinued his research in optics, constructing his first reflectingtelescope in 1669, and wrote a more extended tract on the calculus“De Analysi per Æquations Numero TerminorumInfinitas” incorporating new work on infinite series. On thebasis of this tract Isaac Barrow recommended Newton as his replacementas Lucasian Professor of Mathematics, a position he assumed in October1669, four and a half years after he had received his Bachelor ofArts.

Over the course of the next fifteen years as Lucasian Professor Newtonpresented his lectures and carried on research in a variety ofareas. By 1671 he had completed most of a treatise length accountof the calculus,^[2]which he then found no one would publish. This failure appears to havediverted his interest in mathematics away from the calculus for sometime, for the mathematical lectures he registered during this periodmostly concern algebra. (During the early 1680s he undertook acritical review of classical texts in geometry, a review that reducedhis view of the importance of symbolic mathematics.) His lecturesfrom 1670 to 1672 concerned optics, with a large range of experimentspresented in detail. Newton went public with his work in optics inearly 1672, submitting material that was read before the Royal Societyand then published in thePhilosophical Transactions of the RoyalSociety. This led to four years of exchanges with various figureswho challenged his claims, including both Robert Hooke and ChristiaanHuygens — exchanges that at times exasperated Newton to thepoint that he chose to withdraw from further public exchanges innatural philosophy. Before he largely isolated himself in the late1670s, however, he had also engaged in a series of sometimes longexchanges in the mid 1670s, most notably with John Collins (who had acopy of “De Analysi”) and Leibniz, concerning his work onthe calculus. So, though they remained unpublished, Newton's advancesin mathematics scarcely remained a secret.

This period as Lucasian Professor also marked the beginning of his moreprivate researches in alchemy and theology. Newton purchasedchemical apparatus and treatises in alchemy in 1669, with experimentsin chemistry extending across this entire period. The issue ofthe vows Newton might have to take in conjunction with the LucasianProfessorship also appears to have precipitated his study of thedoctrine of the Trinity, which opened the way to his questioning thevalidity of a good deal more doctrine central to the Roman and AnglicanChurches.

Newton showed little interest in orbital astronomy during this perioduntil Hooke initiated a brief correspondence with him in an effort tosolicit material for the Royal Society at the end of November 1679,shortly after Newton had returned to Cambridge following the death ofhis mother. Among the several problems Hooke proposed to Newtonwas the question of the trajectory of a body under an inverse-squarecentral force:

It now remaines to know the proprietys of a curve Line (not circularnor concentricall) made by a centrall attractive power which makes thevelocitys of Descent from the tangent Line or equall straight motion atall Distances in a Duplicate proportion to the Distances Reciprocallytaken. I doubt not but that by your excellent method you willeasily find out what the Curve must be, and it proprietys, and suggesta physicall Reason of this proportion.^[3]

Newton apparently discovered the systematic relationship betweenconic-section trajectories and inverse-square central forces at thetime, but did not communicate it to anyone, and for reasons thatremain unclear did not follow up this discovery until Halley, during avisit in the summer of 1684, put the same question to him. Hisimmediate answer was, an ellipse; and when he was unable to producethe paper on which he had made this determination, he agreed toforward an account to Halley in London. Newton fulfilled thiscommitment in November by sending Halley a nine-folio-pagemanuscript, “De Motu Corporum in Gyrum” (“On theMotion of Bodies in Orbit”), which was entered into the Registerof the Royal Society in early December 1684. The body of this tractconsists of ten deduced propositions — three theorems and sevenproblems — all of which, along with their corollaries, recur inimportant propositions in thePrincipia.

Save for a few weeks away from Cambridge, from late 1684 until early1687, Newton concentrated on lines of research that expanded the shortten-proposition tract into the 500 pagePrincipia, with its192 derived propositions. Initially the work was to have a twobook structure, but Newton subsequently shifted to three books, andreplaced the original version of the final book with one moremathematically demanding. The manuscript for Book 1 was sent toLondon in the spring of 1686, and the manuscripts for Books 2 and 3, inMarch and April 1687, respectively. The roughly three hundredcopies of thePrincipia came off the press in the summer of1687, thrusting the 44 year old Newton into the forefront of naturalphilosophy and forever ending his life of comparative isolation.

1.3 Newton's Final Years at Cambridge

The years between the publication of thePrincipia andNewton's permanent move to London in 1696 were marked by hisincreasing disenchantment with his situation in Cambridge. In January1689, following the Glorious Revolution at the end of 1688, he waselected to represent Cambridge University in the ConventionParliament, which he did until January 1690. During this time heformed friendships with John Locke and Nicolas Fatio de Duillier, andin the summer of 1689 he finally met Christiaan Huygens face to facefor two extended discussions. Perhaps because of disappointment withHuygens not being convinced by the argument for universal gravity, inthe early 1690s Newton initiated a radical rewriting of thePrincipia. During these same years he wrote (but withheld)his principal treatise in alchemy,Praxis; he correspondedwith Richard Bentley on religion and allowed Locke to read some of hiswritings on the subject; he once again entered into an effort to puthis work on the calculus in a form suitable for publication; and hecarried out experiments on diffraction with the intent of completinghisOpticks, only to withhold the manuscript from publicationbecause of dissatisfaction with its treatment of diffraction. Theradical revision of thePrincipia became abandoned by 1693,during the middle of which Newton suffered, by his own testimony, whatin more recent times would be called a nervous breakdown. In the twoyears following his recovery that autumn, he continued his experimentsin chymistry and he put substantial effort into trying to refine andextend the gravity-based theory of the lunar orbit in thePrincipia, but with less success than he had hoped.

Throughout these years Newton showed interest in a position ofsignificance in London, but again with less success than he had hopeduntil he accepted the relatively minor position of Warden of the Mintin early 1696, a position he held until he became Master of the Mint atthe end of 1699. He again represented Cambridge University inParliament for 16 months, beginning in 1701, the year in which heresigned his Fellowship at Trinity College and the LucasianProfessorship. He was elected President of the Royal Society in1703 and was knighted by Queen Anne in 1705.

1.4 Newton's Years in London and His Final Years

Newton thus became a figure of imminent authority in London over therest of his life, in face-to-face contact with individuals of power andimportance in ways that he had not known in his Cambridge years.His everyday home life changed no less dramatically when hisextraordinarily vivacious teenage niece, Catherine Barton, the daughterof his half-sister Hannah, moved in with him shortly after he moved toLondon, staying until she married John Conduitt in 1717, and after thatremaining in close contact. (It was through her and her husbandthat Newton's papers came down to posterity.) Catherine wassocially prominent among the powerful and celebrated among the literatifor the years before she married, and her husband was among thewealthiest men of London.

The London years saw Newton embroiled in some nasty disputes, probablymade the worse by the ways in which he took advantage of his positionof authority in the Royal Society. In the first years of hisPresidency he became involved in a dispute with John Flamsteed in whichhe and Halley, long ill-disposed toward the Flamsteed, violated thetrust of the Royal Astronomer, turning him into a permanentenemy. Ill feelings between Newton and Leibniz had beendeveloping below the surface from even before Huygens had died in 1695,and they finally came to a head in 1710 when John Keill accused Leibnizin thePhilosophical Transactions of having plagiarized thecalculus from Newton and Leibniz, a Fellow of the Royal Society since1673, demanded redress from the Society. The Society's 1712published response was anything but redress. Newton not only wasa dominant figure in this response, but then published an outspokenanonymous review of it in 1715 in thePhilosophicalTransactions. Leibniz and his colleagues on the Continenthad never been comfortable with thePrincipia and itsimplication of action at a distance. With the priority disputethis attitude turned into one of open hostility toward Newton's theoryof gravity — a hostility that was matched in its blindness by thefervor of acceptance of the theory in England. The publicelements of the priority dispute had the effect of expanding a schismbetween Newton and Leibniz into a schism between the English associatedwith the Royal Society and the group who had been working with Leibnizon the calculus since the 1690s, including most notably JohannBernoulli, and this schism in turn transformed into one between theconduct of science and mathematics in England versus the Continent thatpersisted long after Leibniz died in 1716.

Although Newton obviously had far less time available to devote tosolitary research during his London years than he had had inCambridge, he did not entirely cease to be productive. The first(English) edition of hisOpticks finally appeared in 1704,appended to which were two mathematical treatises, his first work onthe calculus to appear in print. This edition was followed by a Latinedition in 1706 and a second English edition in 1717, each containingimportant Queries on key topics in natural philosophy beyond those inits predecessor. Other earlier work in mathematics began to appear inprint, including a work on algebra,Arithmetica Universalis,in 1707 and “De Analysi” and a tract on finitedifferences, “Methodis differentialis” in 1711. The secondedition of thePrincipia, on which Newton had begun work atthe age of 66 in 1709, was published in 1713, with a third edition in1726. Though the original plan for a radical restructuring had longbeen abandoned, the fact that virtually every page of thePrincipia received some modifications in the second editionshows how carefully Newton, often prodded by his editor Roger Cotes,reconsidered everything in it; and important parts were substantiallyrewritten not only in response to Continental criticisms, but alsobecause of new data, including data from experiments on resistanceforces carried out in London. Focused effort on the third editionbegan in 1723, when Newton was 80 years old, and while the revisionsare far less extensive than in the second edition, it does containsubstantive additions and modfications, and it surely has claim tobeing the edition that represents his most considered views.

Newton died on 20 March 1727 at the age of 84. Hiscontemporaries' conception of him nevertheless continued to expand as aconsequence of various posthumous publications, includingTheChronology of Ancient Kingdoms Amended (1728); the work originallyintended to be the last book of thePrincipia,The Systemof the World (1728, in both English and Latin);Observationsupon the Prophecies of Daniel and the Apocalypse of St. John(1733);A Treatise of the Method of Fluxions and InfiniteSeries (1737);A Dissertation upon the Sacred Cubit of theJews (1737), andFour Letters from Sir Isaac Newton to DoctorBentley concerning Some Arguments in Proof of a Deity(1756). Even then, however, the works that had been publishedrepresented only a limited fraction of the total body of papers thathad been left in the hands of Catherine and John Conduitt. Thefive volume collection of Newton's works edited by Samuel Horsley(1779–85) did not alter this situation. Through the marriage ofthe Conduitts' daughter Catherine and subsequent inheritance, this bodyof papers came into the possession of Lord Portsmouth, who agreed in1872 to allow it to be reviewed by scholars at Cambridge University(John Couch Adams, George Stokes, H. R. Luard, and G. D.Liveing). They issued a catalogue in 1888, and the universitythen retained all the papers of a scientific character. With thenotable exception of W. W. Rouse Ball, little work was done on thescientific papers before World War II. The remaining papers werereturned to Lord Portsmouth, and then ultimately sold at auction in1936 to various parties. Serious scholarly work on them did notget underway until the 1970s, and much remains to be done on them.

2. Newton's Work and Influence

Three factors stand in the way of giving an account of Newton's workand influence. First is the contrast between the public Newton,consisting of publications in his lifetime and in the decade or twofollowing his death, and the private Newton, consisting of hisunpublished work in math and physics, his efforts in chymistry —that is, the 17th century blend of alchemy and chemistry — andhis writings in radical theology — material that has becomepublic mostly since World War II. Only the public Newton influencedthe eighteenth and early nineteenth centuries, yet any account ofNewton himself confined to this material can at best be onlyfragmentary. Second is the contrast, often shocking, between theactual content of Newton's public writings and the positionsattributed to him by others, including most importantly hispopularizers. The term “Newtonian” refers to severaldifferent intellectual strands unfolding in the eighteenth century,some of them tied more closely to Voltaire, Pemberton, and Maclaurin— or for that matter to those who saw themselves as extendinghis work, such as Clairaut, Euler, d'Alembert, Lagrange, and Laplace— than to Newton himself. Third is the contrast between theenormous range of subjects to which Newton devoted his fullconcentration at one time or another during the 60 years of hisintellectual career — mathematics, optics, mechanics, astronomy,experimental chemistry, alchemy, and theology — and theremarkably little information we have about what drove him or hissense of himself. Biographers and analysts who try to piece together aunified picture of Newton and his intellectual endeavors often end uptelling us almost as much about themselves as about Newton.

Compounding the diversity of the subjects to which Newton devoted timeare sharp contrasts in his work within each subject. Optics andorbital mechanics both fall under what we now call physics, and eventhen they were seen as tied to one another, as indicated by Descartes'first work on the subject,Le Monde, ou Traité de lalumierè. Nevertheless, two very different“Newtonian” traditions in physics arose from Newton'sOpticks andPrincipia: from hisOpticks atradition centered on meticulous experimentation and from hisPrincipia a tradition centered on mathematical theory. Themost important element common to these two was Newton's deepcommitment to having the empirical world serve not only as theultimate arbiter, but also as the sole basis for adopting provisionaltheory. Throughout all of this work he displayed distrust of what wasthen known as the method of hypotheses – putting forwardhypotheses that reach beyond all known phenomena and then testing themby deducing observable conclusions from them. Newton insisted insteadon having specific phenomena decide each element of theory, with thegoal of limiting the provisional aspect of theory as much as possibleto the step of inductively generalizing from the specificphenomena. This stance is perhaps best summarized in his fourth Ruleof Reasoning, added in the third edition of thePrincipia,but adopted as early as his Optical Lectures of the 1670s:

In experimental philosophy, propositions gathered from phenomenaby induction should be taken to be either exactly or very nearly truenotwithstanding any contrary hypotheses, until yet other phenomena makesuch propositions either more exact or liable to exceptions.

This rule should be followed so that arguments based oninduction may not be nullified by hypotheses.

Such a commitment to empirically driven science was a hallmark ofthe Royal Society from its very beginnings, and one can find it in theresearch of Kepler, Galileo, Huygens, and in the experimental effortsof the Royal Academy of Paris. Newton, however, carried thiscommitment further first by eschewing the method of hypotheses andsecond by displaying in hisPrincipia andOpticks howrich a set of theoretical results can be secured through well-designedexperiments and mathematical theory designed to allow inferences fromphenomena. The success of those after him in building on thesetheoretical results completed the process of transforming naturalphilosophy into modern empirical science.

Newton's commitment to having phenomena decide the elements oftheory required questions to be left open when no available phenomenacould decide them. Newton contrasted himself most strongly withLeibniz in this regard at the end of his anonymous review of the RoyalSociety's report on the priority dispute over the calculus:

It must be allowed that these two Gentlemen differ very much inPhilosophy. The one proceeds upon the Evidence arising fromExperiments and Phenomena, and stops where such Evidence is wanting;the other is taken up with Hypotheses, and propounds them, not to beexamined by Experiments, but to be believed without Examination.The one for want of Experiments to decide the Question, doth not affirmwhether the Cause of Gravity be Mechanical or not Mechanical; the otherthat it is a perpetual Miracle if it be not Mechanical.

Newton could have said much the same about the question of whatlight consists of, waves or particles, for while he felt that the latterwas far more probable, he saw it still not decided by any experiment orphenomenon in his lifetime. Leaving questions about the ultimatecause of gravity and the constitution of light open was the otherfactor in his work driving a wedge between natural philosophy andempirical science.

The many other areas of Newton's intellectual endeavors made less of adifference to eighteenth century philosophy and science. Inmathematics, Newton was the first to develop a full range ofalgorithms for symbolically determining what we now call integrals andderivatives, but he subsequently became fundamentally opposed to theidea, championed by Leibniz, of transforming mathematics into adiscipline grounded in symbol manipulation. Newton thought the onlyway of rendering limits rigorous lay in extending geometry toincorporate them, a view that went entirely against the tide in thedevelopment of mathematics in the eighteenth and nineteenthceturies. In chemistry Newton conducted a vast array of experiments,but the experimental tradition coming out of hisOpticks, andnot his experiments in chemistry, lay behind Lavoisier calling himselfa Newtonian; indeed, one must wonder whether Lavoisier would even haveassociated his new form of chemistry with Newton had he been aware ofNewton's fascination with writings in the alchemical tradition. Andeven in theology, there is Newton the anti-Trinitarian mild hereticwho was not that much more radical in his departures from Roman andAnglican Christianity than many others at the time, and Newton, thewild religious zealot predicting the end of the Earth, who did notemerge to public view until quite recently.

There is surprisingly little cross-referencing of themes from one areaof Newton's endeavors to another. The common element across almost allof them is that of a problem-solverextraordinaire, taking onone problem at a time and staying with it until he had found, usuallyrather promptly, a solution. All of his technical writings displaythis, but so too does his unpublished manuscript reconstructingSolomon's Temple from the biblical account of it and his posthumouslypublishedChronology of the Ancient Kingdoms in which heattempted to infer from astronomical phenomena the dating of majorevents in the Old Testament. The Newton one encounters in his writingsseems to compartmentalize his interests at any given moment. Whetherhe had a unified conception of what he was up to in all hisintellectual efforts, and if so what this conception might be, hasbeen a continuing source of controversy among Newton scholars.

Of course, were it not for thePrincipia, there would be noentry at all for Newton in an Encyclopedia of Philosophy. In science,he would have been known only for the contributions he made to optics,which, while notable, were no more so than those made by Huygens andGrimaldi, neither of whom had much impact on philosophy; and inmathematics, his failure to publish would have relegated his workto not much more than a footnote to the achievements of Leibniz andhis school. Regardless of which aspect of Newton's endeavors“Newtonian” might be applied to, the word gained its aurafrom thePrincipia. But this adds still a furthercomplication, for thePrincipia itself was substantiallydifferent things to different people. The press-run of the firstedition (estimated to be around 300) was too small for it to have beenread by all that many individuals. The second edition also appeared intwo pirated Amsterdam editions, and hence was much more widelyavailable, as was the third edition and its English (and laterFrench) translation. ThePrincipia, however, is not an easybook to read, so one must still ask, even of those who had access toit, whether they read all or only portions of the book and to whatextent they grasped the full complexity of what they read. Thedetailed commentary provided in the three volume Jesuit edition(1739–42) made the work less daunting. But even then the vast majorityof those invoking the word “Newtonian” were unlikely tohave been much more conversant with thePrincipia itself thanthose in the first half of the 20th century who invoked‘relativity’ were likely to have read Einstein's twospecial relativity papers of 1905 or his general relativity paper of1916. An important question to ask of any philosophers commenting onNewton is, what primary sources had they read?

The 1740s witnessed a major transformation in the standing of thescience in thePrincipia. ThePrincipia itselfhad left a number of loose-ends, most of them detectable by only highlydiscerning readers. By 1730, however, some of these loose-endshad been cited in Bernard le Bovier de Fontenelle's elogiumfor Newton^[4] and inJohn Machin's appendix to the 1729 English translation of thePrincipia, raising questions about just how secure Newton'stheory of gravity was, empirically. The shift on the continent beganin the 1730s when Maupertuis convinced the Royal Academy to conductexpeditions to Lapland and Peru to determine whether Newton's claimsabout the non-spherical shape of the Earth and the variation ofsurface gravity with latitude are correct. Several of the loose-endswere successfully resolved during the 1740's through such notableadvances beyond thePrincipia as Clairaut'sThéorie de la Figure de la Terre; the return of theexpedition from Peru; d'Alembert's 1749 rigid-body solution for thewobble of the Earth that produces the precession of the equinoxes;Clairaut's 1749 resolution of the factor of 2 discrepancy betweentheory and observation in the mean motion of the lunar apogee, glossedover by Newton but emphasized by Machin; and the prize-winning firstever successful description of the motion of the Moon by Tobias Mayerin 1753, based on a theory of this motion derived from gravity byEuler in the early 1750s taking advantage of Clairaut's solution forthe mean motion of the apogee.

Euler was the central figure in turning the three laws of motion putforward by Newton in thePrincipia into Newtonianmechanics. These three laws, as Newton formulated them, apply to“point-masses,” a term Euler had put forward in hisMechanica of 1736. Most of the effort of eighteenth centurymechanics was devoted to solving problems of the motion of rigidbodies, elastic strings and bodies, and fluids, all of which requireprinciples beyond Newton's three laws. From the 1740s on this led toalternative approaches to formulating a general mechanics, employingsuch different principles as the conservation ofvis viva,the principle of least action, and d'Alembert's principle. The“Newtonian” formulation of a general mechanics sprang fromEuler's proposal in 1750 that Newton's second law, in anF=maformulation that appears nowhere in thePrincipia, could beapplied locally within bodies and fluids to yield differentialequations for the motions of bodies, elastic and rigid, andfluids. During the 1750s Euler developed his equations for the motionof fluids, and in the 1760s, his equations of rigid-bodymotion. What we call Newtonian mechanics was accordingly something forwhich Euler was more responsible than Newton.

Although some loose-ends continued to defy resolution until much laterin the eighteenth century, by the early 1750s Newton's theory ofgravity had become the accepted basis for ongoing research amongalmost everyone working in orbital astronomy. Clairaut's successfulprediction of the month of return of Halley's comet at the end of thisdecade made a larger segment of the educated public aware of theextent to which empirical grounds for doubting Newton's theory ofgravity had largely disappeared. Even so, one must still ask of anyoneoutside active research in gravitational astronomy just how aware theywere of the developments from ongoing efforts when they made theirvarious pronouncements about the standing of the science of thePrincipia among the community of researchers. The naivety ofthese pronouncements cuts both ways: on the one hand, they oftenreflected a bloated view of how secure Newton's theory was at thetime, and, on the other, they often underestimated how strong theevidence favoring it had become. The upshot is a need to be attentiveto the question of what anyone, even including Newton himself, had inmind when they spoke of the science of thePrincipia.

To view the seventy years of research after Newton died as merely tyingup the loose-ends of thePrincipia or as simply compiling moreevidence for his theory of gravity is to miss the whole point.Research predicated on Newton's theory had answered a huge numberof questions about the world dating from long before it. Themotion of the Moon and the trajectories of comets were two earlyexamples, both of which answered such questions as how one cometdiffers from another and what details make the Moon's motion somuch more complicated than that of the satellites of Jupiter andSaturn. In the 1770s Laplace had developed a proper theory of thetides, reaching far beyond the suggestions Newton had made in thePrincipia by including the effects of the Earth'srotation and the non-radial components of the gravitational forces ofthe Sun and Moon, components that dominate the radial component thatNewton had singled out. In 1786 Laplace identified a large 900year fluctuation in the motions of Jupiter and Saturn arising fromquite subtle features of their respective orbits. With thisdiscovery, calculation of the motion of the planets from the theory ofgravity became the basis for predicting planet positions, withobservation serving primarily to identify further forces not yet takeninto consideration in the calculation. These advances in ourunderstanding of planetary motion led Laplace to produce the fourprincipal volumes of hisTraité de mécaniquecéleste from 1799 to 1805, a work collecting in one placeall the theoretical and empirical results of the research predicated onNewton'sPrincipia. From that time forward,Newtonian science sprang from Laplace's work, notNewton's.

The success of the research in celestial mechanics predicated on thePrincipia was unprecedented. Nothing of comparable scopeand accuracy had ever occurred before in empirical research of anykind. That led to a new philosophical question: what was it aboutthe science of thePrincipia that enabled it to achieve whatit did? Philosophers like Locke and Berkeley began asking thisquestion while Newton was still alive, but it gained increasing forceas successes piled on one another over the decades after he died.This question had a practical side, as those working in other fieldslike chemistry pursued comparable success, and others like Hume andAdam Smith aimed for a science of human affairs. It had, ofcourse, a philosophical side, giving rise to the subdiscipline ofphilosophy of science, starting with Kant and continuing throughout thenineteenth century as other areas of physical science began showingsimilar signs of success. The Einsteinian revolution in thebeginning of the twentieth century, in which Newtonian theory was shownto hold only as a limiting case of the special and general theories ofrelativity, added a further twist to the question, for now all thesuccesses of Newtonian science, which still remain in place, have to beseen as predicated on a theory that holds only to high approximation inparochial circumstances.

The extraordinary character of thePrincipia gave riseto a still continuing tendency to place great weight on everythingNewton said. This, however, was, and still is, easy to carry toexcess. One need look no further than Book 2 of thePrincipia to see that Newton had no more claim to beingsomehow in tune with nature and the truth than any number of hiscontemporaries. Newton's manuscripts do reveal an exceptionallevel of attention to detail of phrasing, from which we can rightlyconclude that his pronouncements, especially in print, weregenerally backed by careful, self-critical reflection.But this conclusion does not automatically extend to every statement heever made. We must constantly be mindful of the possibility oftoo much weight being placed, then or now, on any pronouncement thatstands in relative isolation over his 60 year career; and, to counterthe tendency to excess, we should be even more vigilant than usual innot losing sight of the context, circumstantial as well as historicaland textual, of both Newton's statements and the eighteenth centuryreaction tothem.

Bibliography

Primary Sources

Secondary Sources

• Westfall, Richard S., 1980,Never At Rest: A Biography of IsaacNewton, New York: Cambridge University Press.
• Hall, A. Rupert, 1992,Isaac Newton:Adventurer in Thought, Oxford: Blackwell.
• Feingold, Mordechai, 2004,The NewtonianMoment: Isaac Newton and the Making of Modern Culture, Oxford:Oxford University Press.
• Iliffe, Rob, 2007,Newton: A Very Short IntroductionOxford: Oxford University Press.
• Cohen, I. B. and Smith, G. E., 2002,The Cambridge Companionto Newton, Cambridge: Cambridge University Press.
• Cohen, I. B. and Westfall, R. S., 1995,Newton: Texts,Backgrounds, and Commentaries, A Norton Critical Edition, NewYork: Norton.

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