NEWTON, ISAAC

(b. Woolsthorpe, England, 25 December 1642; d. London, England, 20 March 1727)

mathematics, dynamics, celestial mechanics, astronomy, optics, natural philosophy. For the original article on Newton, see DSB, vol. 10.

Since I.B. Cohen’s entry in the original DSB (1974), careful study and analysis of Newton’s manuscripts has revised our understanding of all aspects of his life and work. In the first part of this Postscript, George Smith describes recent historical work on Newton’s mathematics, optics, and mechanics. In the second section, William Newman discusses the new research on Newton’s alchemy and matter theory.

New Collections of Newton’s Papers I. B. Cohen noted in the original DSB (1974) that three volumes remained to be published in both The Mathematical Papers of Isaac Newton, edited by D. T. Whiteside (vols. VI–VII, covering the period from 1684), and The Correspondence of Isaac Newton (vols. V–VII, covering from 1709). Cohen also noted that much work remained to be done on Newton’s unpublished manuscripts, some of which has now been carried out. As much studied as Newton had been at the time of Cohen’s comprehensive entry, the publication of these volumes, together with Volume 1 of The Optical Papers of Isaac Newton (ed. A. E. Shapiro, 1984) and R. S. Westfall’s intellectual biography, Never at Rest (1980), has led to a deeper understanding of Newton’s scientific work, especially concerning his own view of that work. The advances are summarized below in the sequence Cohen followed: mathematics, optics, and the Principia.

Mathematics The last three volumes of The Mathematical Papers have provided a much richer picture of the geometrical mathematics that Newton had settled on during the 1680s. Whiteside’s annotations in Volume VI covering the mathematics of Book 1 of the Principia bring out the relation between the geometry with limits that Newton employed there and the Leibnizian symbolic calculus that subsequently came to dominate “Newtonian” mechanics. Still more important are the more than five hundred pages in Volume VII that present Newton’s never completed Geometria of the early 1690s. The goal of this work was to start from the foundations of elementary classical geometry, ultimately developing with full rigor the fluxional methods of Newton’s calculus, but within a strictly geometrical framework. This work shows that Newton’s preference for geometric over symbolic mathematics involved more than geometry’s claim to higher standards of rigor or his predilection for the wisdom of the ancients. In his Arithmetica Universalis he had already derived algebraic methods out of elementary arithmetic, establishing their rigor so far as these methods go. Newton, however, did not see how limits could be added to symbolic mathematics in a fully rigorous manner, while geometry (as his Geometria was going to show) allowed limits to be added rigorously; and the constructions of synthetic geometry have a claim to exactness that the incommensurability of irrational numbers prevented symbolic mathematics from matching when symbols are taken to stand in for numbers, as they are in Arithmetica Universalis, rather than for geometric magnitudes.

Volume VIII of Mathematical Papers primarily concerns the controversy with Leibniz over priority to the calculus, examined in detail in A. R. Hall’s Philosophers at War(1980). Newton without question was the first to develop what, following Leibniz, we now call the calculus, but Leibniz developed it independently, in the process coming to promote symbolic methods as preferable to geometry, primarily because they make discoveries much easier. One has to wonder how different the history of mathematics might have been if Newton had found a publisher for his extensive treatise De Methodis Serium et Fluxionum in 1672, before Leibniz had made his discoveries.

Optics Newton’s Optical Lectures of 1670–1672 (Optical Papers, vol. I) supplement the original DSB account of his work in optics in two ways. First, they reveal that the extensive experiments described in his published papers on colors in the 1670s and Book I of the Opticks comprise only a fraction of the total experiments he performed on refraction. The further experiments generally served to cross-check the results of the principal experiments or to pave the way to them. The full range of experiments thus shows how meticulous an experimenter Newton was. Second, the Lectures contain a passage showing that, long before the Principia, he viewed mathematical principles as crucial to scientific knowledge:

Indeed, since an exact science of them [colors] seems to be one of the most difficult that philosophy is in need of, I hope to show—as it were, by my example—how valuable mathematics is in natural philosophy. I therefore urge geometers to investigate nature more rigorously, and those devoted to natural science to learn geometry first.…[W]ith the help of philosophical geometers and geometrical philosophers, instead of the conjectures and probabilities that are being bla-zoned about everywhere, we shall finally achieve a natural science supported by the greatest evidence. (Optical Papers, vol. I, p. 87)

Although A. E. Shapiro is still preparing the second volume of the Optical Papers, his Fits, Passions, and Paroxysms(1993) has already described Newton’s struggle to produce the theory presented in Books II and III of the Opticks of such periodic phenomena as “Newton’s rings” and Grimaldi’s “fringes.” In addition to complicating the commonplace conception of Newton as a proponent of a corpuscular theory of light, Shapiro’s book displays once more Newton’s commitment to having the empirical world decide questions.

Principia I. B. Cohen’s “A Guide to Newton’s Principia,” which accompanies his and Anne Whitman’s new translation, has updated his original DSB account of the book. The combination of this “Guide” with Whiteside’s explanatory notes in Volume VI of Mathematical Papers has made the recondite details of the Principia much more accessible. Recent research that builds on the work of Cohen and Whiteside has also added new dimensions to some long-standing disputes generated by the book, the most important of which will be summarized here.

Although Newton undoubtedly found absolute space an indispensable heuristic for conceptualizing absolute motion, efforts by physicists to reformulate Newtonian theory in a relativistic space-time framework have made clear that the empirical science of the Principia does not presuppose it. It presupposes a Euclidean three-dimensional affine space, with time separate. As Corollaries 5 and 6 to the Laws of Motion make clear, the book cannot provide means for distinguishing rest from absolute uniform motion in a straight line, or even absolute accelerated motion in which all accessible bodies are undergoing the same acceleration in a straight line. What it does claim is that the forces that cause them enable absolute, real changes of motion, especially curvilinear changes, to be distinguished from relative, merely apparent changes of motion. The Newtonian assumptions in conflict with Einstein’s theory, besides Euclidean space, involve always in principle being able first to settle any question about the simultaneity of two events and, second, to distinguish between uniformly accelerated free-fall and inertial motion. This partial rapprochement with Einstein, first developed by Howard Stein in 1968, has been laid out more recently in Robert DiSalle’s Understanding Space-Time.

In Book 1, Newton seems in places to gloss over the difference between discrete forces, or impulses, and continuously acting forces. His use of proportions rather than equations allows him to avoid dimensional inconsistencies in doing so, but questions still arise about his employing motions governed by impulses to reach conclusions about motions governed by continuous forces. Bruce Pourciau has shown that Newton was making an implicit assumption that can be proved, but not by methods known to him: every motion generated by a centripetal force acting uninterruptedly for a given time is the limiting case of motions generated by centripetal impulses. Some have also argued that Newton’s laws of motion were formulated strictly for discrete forces without his ever justifying their application to continuous forces. Pourciau has now shown that the second law, as Newton conceived it, holds for both discrete and continuous forces. In a manuscript first published in Volume 6 of Mathematical Papers (p. 539ff), Newton explained that his measure of the “change of motion” referred to in the law is the distance after a given time between where the given body is and where it would have been had it proceeded inertially; under this measure (with the “evanescent” increments of time of Lemma 10 serving in the case of nonuniform continuous forces), Newton’s law applies to both types of force.

The importance to the Principia of some less discussed parts of Book 1 has now become clearer. Newton introduced a second method for inferring rules of force from motions in the second edition, employing curvature: force varies as v²/(r sin ?), where ? is the angle between the tangent to the trajectory and the radius vector to the center of force, in contrast to the familiar v²/r for uniform circular motion that he and Huygens had independently discovered decades earlier. Michael Nauenberg and Bruce Brackenridge have shown that Newton was already in full command of, and in places took important advantage of, these curvature methods in the first edition. The scope and power of the results on precessing orbits in Section 9 have been spelled out, primarily in papers by S. R. Valluri and colleagues. And Section 10 on constrained motion has now been shown to make a crucial contribution to the book. Newton’s “Moon Test,” showing terrestrial gravity extends to the Moon, employs Huygens’s pendulum measure of surface gravity. This measure presupposes uniform gravity acting along parallel lines, in prima facie conflict with Newton’s inverse-square centripetal gravity. Section 10 legitimates this measure by showing that it, and Galilean gravity generally, hold in the limit at the surface of a uniformly dense sphere or spheroid as its radius becomes indefinitely large—in much the manner of Einstein’s proof that Newtonian gravity holds in the static weak-field limit of his new theory of gravity.

All but the last two sections of Book II concern motion in resisting media. The conclusion that Newton wanted to draw has always been clear: the absence of any sign of such forces in the motions of the planets and comets shows that the celestial regions are free of the sort of fluid required by Descartes’ and Leibniz’s vortex theories of celestial motion. To show this, Newton had to show that the density and hence inertia of any fluid medium gives rise to forces of resistance. What has now become clearer is how much of the effort of Book II is devoted to disaggregating the contribution to resistance made by the inertia of the fluid from the contributions made by its viscosity and friction between it and a moving body. In the first edition Newton had hoped that pendulum-decay experiments could directly disaggregate the inertial resistance, but the results fell short of his standards, leading him to add vertical-fall experiments in the next two editions. The data from these vertical-fall experiments were of very high quality, but they did not directly disaggregate the inertial contribution, leaving a lacuna in his reasoning later exposed by d’Alembert.

Newton’s claim to having “deduced” the law of gravity from phenomena of orbital motion in Book 3 has been the subject of much analysis over the last thirty years. Howard Stein and Dana Densmore have called attention to the one real lacuna in this “deduction” (Proposition 5, Corollary 1, as originally noted by Roger Cotes while he was editing the second edition); William Harper has shown how well the other steps in the reasoning stand up to scrutiny; and George Smith has emphasized how Newton was employing approximative reasoning throughout, with his Rules of Reasoning then providing the license to take (Newton’s word) the law to be exact.

Two further advances have been made with the rest of Book 3. Newton revised Propositions 19 and 20 on the variation of surface gravity with latitude and the figure of the Earth twice, reaching three different conclusions in the three editions. We now see why Newton viewed them as so important. Christiaan Huygens recognized that these are the only (then) empirically accessible results in the Principia that presuppose gravity between every two particles of matter. In replying to the book in his Discourse on the Cause of Gravity (1690), he devised an experimentum crucis around these results and announced that he had evidence from pendulum-clock measurements at sea refuting Newton. This also clarifies why these propositions became so important during the 1730s and 1740s. Finally, Curtis Wilson and others have clarified how large a gap remained between Newton’s quantitative efforts on the lunar orbit and later eighteenth-century work, as has D. E. Cartwright for the gap in the case of the tides.

SUPPLEMENTARBLIOGRAPHY

WORKS BY NEWTON PUBLISHED AFTER 1974

Certain Philosophical Questions: Newton’s Trinity Notebook, edited by J. E. McGuire and M. Tamny. Cambridge, U.K.: Cambridge University Press, 1983.

The Correspondence of Isaac Newton, vols. V–VII, edited by A. R. Hall and L. Tilling. Cambridge, U.K.: Cambridge University Press, 1975, 1976, 1977.

Isaac Newton’s Papers and Letters on Natural Philosophy. 2^nd ed. Cambridge, MA: Harvard University Press, 1978.

The Mathematical Papers of Isaac Newton, vols. VI–VIII, edited by D. T. Whiteside. Cambridge, U.K.: Cambridge University Press, 1974, 1976, 1981.

The Optical Papers of Isaac Newton, vol. 1, edited and translated by A. E. Shapiro. Cambridge, U.K.: Cambridge University Press, 1984. The first of two projected volumes.

Philosophical Writings, edited by A. Janiak. Cambridge, U.K.: Cambridge University Press, 2004. Newton’s philosophical writings in English translation.

The Preliminary Manuscripts for Isaac Newton’s 1687 Principia, 1684–1686. Cambridge, U.K.: Cambridge University Press, 1989.

The Principia, Mathematical Principles of Natural Philosophy: A New Translation, translated by I. B. Cohen and A. Whitman. Berkeley, Los Angeles, and London: University of California Press, 1999.

OTHER SOURCES PUBLISHED AFTER 1974

Biographical and Bibliographical

Gjertsen, Derek. The Newton Handbook. London and New York: Routledge & Kegan Paul, 1986.

Hall, A. Rupert. Isaac Newton, Adventurer in Thought. Oxford: Blackwell, 1992.

Hall, A. Rupert, ed. Isaac Newton, Eighteenth-Century Perspectives: A Collection of Early Biographical Memoirs. Oxford: Oxford University Press, 1999.

Harrison, John. The Library of Isaac Newton. Cambridge, U.K.: Cambridge University Press, 1978.

Wallis, Peter, and Ruth Wallis. Newton and Newtoniana, 1672–1975: A Bibliography. London: Dawsons, 1977.

Westfall, Richard Samuel. Never at Rest: A Biography of Isaac Newton. Cambridge, U.K.: Cambridge University Press, 1983.

Collections of Studies Bechler, Zev, ed. Contemporary Newtonian Scholarship. Dordrecht, Boston, and London: D. Reidel, 1982.

Buchwald, Jed, and I. Bernard Cohen, eds. Isaac Newton’s Natural Philosophy. Cambridge, MA: MIT Press, 2001.

Cohen, I. Bernard, and Richard S. Westfall. Newton: Texts, Backgrounds, and Commentaries, A Norton Critical Edition. New York and London: W. W. Norton, 1995.

Cohen, I. Bernard, and George E. Smith, eds. The Cambridge Companion to Newton. Cambridge, U.K.: Cambridge University Press, 2002.

Dalitz, Richard H., and Michael Nauenberg, eds. The Foundations of Newtonian Scholarship. Singapore: World Scientific, 2000.

Durham, F., and R. D. Puddington, eds. Some Truer Method: Reflections on the Heritage of Newton. New York: Columbia University Press, 1990.

Fauvel, John, Raymond Flood, Michael Shortland, and Robin Wilson, eds. Let Newton Be! A New Perspective on His Life and Works. Oxford and New York: Oxford University Press, 1988.

Harman, P. M., and Alan E. Shapiro. The Investigation of Difficult Things: Essays on Newton and the History of the Exact Sciences. Cambridge, U.K.: Cambridge University Press, 1992.

King-Hele, D. G., and A. R. Hall, eds. Newton's Principia and Its Legacy. Proceedings of a Royal Society Discussion Meeting of 30 June 1987. London: The Royal Society, 1988.

Theerman, P. and A. F. Seef, eds. Action and Reaction. Newark, Delaware: University of Delaware Press, 1993.

Mathematics

Guicciardini, Niccolò. The Development of Newtonian Calculus in Britain, 1700–1800. Cambridge, U.K.: Cambridge University Press, 1989.

—_____. Reading the Principia: The Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736. Cambridge, U.K.: Cambridge University Press, 1999.

Hall, A. Rupert. Philosophers at War: The Quarrel Between Newton and Leibniz. Cambridge, U.K.: Cambridge University Press, 1980.

Pourciau, Bruce. “The Preliminary Mathematical Lemmas of Newton’s Principia.” Archive for History of Exact Sciences 52 (1998): 279–295.

Optics

Hall, A. Rupert. And All Was Light: An Introduction to Newton’s Opticks. Oxford: Clarendon Press, 1993.

Schaffer, Simon. “Glass Works: Newton’s Prisms and the Use of Experiment.” In The Use of Experiment: Studies in the Natural Sciences, edited by David Gooding, Trevor Pinch, and Simon Schaffer, pp. 67–104. Cambridge: Cambridge University Press, 1989.

Shapiro, Alan E. Fits, Passions, and Paroxysms: Physics, Method, and Chemistry and Newton’s Theories of Colored Bodies and Fits of Easy Reflection. Cambridge, U.K.: Cambridge University Press, 1993.

_____. The Evolving Structure of Newton’s Theory of White Light and Color: 1670–1704.” Isis 71 (1980): 211–235.

_____. The Gradual Acceptance of Newton’s Theory of Light and Color,” Perspectives on Science 4 (1996), pp. 59-104.

_____. Newton’s Experimental Investigation of Diffraction for the Opticks: A Preliminary Study.” In The Foundations of Newtonian Scholarship, edited by R. H. Dalitz and M. Nauenberg, pp. 29–56. Singapore: World Scientific, 2000.

_____. Newton’s Optics and Atomism.” In The Cambridge Companion to Newton, edited by I. B. Cohen and G. E. Smith, pp. 227-255. Cambridge, U.K.: Cambridge University Press, 2002.

The Principia

Bertoloni Meli, Dominico. Equivalence and Priority: Newton versus Leibniz. Oxford: Clarendon Press, 1993. —_____. Thinking with Objects: The Transformation of Mechanics in the Sevententh Century. Baltimore, MD: The Johns Hopkins University Press, 2006.

Brackenridge, J. Bruce, and Michael Nauenberg. “Curvature in Newton’s Dynamics.” In The Cambridge Companion to Newton, edited by I. B. Cohen and G. E. Smith, pp. 85–137. Cambridge, U.K.: Cambridge University Press, 2002.

Cartwright, David Edgar. Tides: A Scientific History. Cambridge, U.K.: Cambridge University Press, 1999.

Chandrasekhar, S. Newton’s Principia for the Common Reader. Oxford: Clarendon Press, 1995.

Cohen, I. Bernard. The Newtonian Revolution. Cambridge, U.K., and New York: Cambridge University Press, 1980.

DiSalle, Robert. Understanding Space-Time: The Philosophical Development of Physics from Newton to Einstein. Cambridge, U.K.: Cambridge University Press, 2006.

Greenberg, Daniel L. The Problem of the Earth’s Shape from Newton to Clairaut. Cambridge, U.K.: Cambridge University Press, 1995.

Harper, William. “Isaac Newton on Empirical Success and Scientific Method.” In The Cosmos of Science: Essays of Exploration, edited by John Earman and John D. Norton, pp. 55–86. Pittsburgh: University of Pittsburgh Press, 1997.

_____. Howard Stein on Isaac Newton: Beyond Hypotheses?” In Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics, edited by D. B. Malament, pp. 71–112. Chicago: Open Court, 2002.

Nauenberg, Michael. “Newton’s Early Computational Method for Dynamics.” Archive for History of Exact Sciences 46 (1994): 221–252.

Pourciau, Bruce. “Newton’s Argument for Proposition 1 of the Principia.” Archive for History of Exact Sciences 57 (2003): 267–311.

_____. The Importance of Being Equivalent: Newton’s Two Models of One-Body Motion.” Archive for History of Exact Sciences 58 (2004): 283–321. _____. Newton’s Interpretation of Newton’s Second Law.” Archive for History of Exact Sciences 60 (2006): 157–207.

Schliesser, Eric, and G. E. Smith. “Huygens’s 1688 Report to the Dutch East India Company on the Measurement of Longitude at Sea and the Evidence It Offered Against

Universal Gravity.” Archive for History of Exact Sciences, forthcoming.

Smeenk, Christopher, and G. E. Smith. “Newton on Constrained Motion: A Commentary on Book 1 Section 10 of the Principia.” Archive for History of Exact Sciences, forthcoming.

Smith, George E. “The Newtonian Style in Book II of the Principia.” In Isaac Newton’s Natural Philosophy, edited by J. Z. Buchwald and I. B. Cohen, pp. 249–313. Cambridge, MA: MIT Press, 2001

. _____. How Did Newton Discover Universal Gravity?” In Beyond Hypothesis: Newton’s Experimental Philosophy. Proceedings of a Conference at St. John’s College, Annapolis. The St. John’s Review XLV (1999): 32–63.

_____. From the Phenomenon of the Ellipse to an Inverse-Square Force: Why Not?” In Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics, edited by D. B. Malament, pp. 31–70. Chicago: Open Court, 2002.

_____. The Methodology of the Principia.” In The Cambridge Companion to Newton, edited by I. B. Cohen and G. E. Smith, pp. 138–173. Cambridge, U.K.: Cambridge University Press, 2002.

Stein, Howard. “Some Philosophical Prehistory of General Relativity.” In Minnesota Studies in the Philosophy of Science, vol. VIII, Foundations of Space-Time Theories, edited by J. Earman, C. Glymour, and J. Stachel, pp. 3–49. Minneapolis: University of Minnesota Press, 1977.

_____. ‘From the Phenomena of Motions to the Forces of Nature’: Hypothesis or Deduction?” PSA 1990. Proceedings of the 1990 Biennial Meeting of the Philosophy of Science Association, vol. 2, pp. 209–222. East Lansing: Philosophy of Science Association, 1991.

_____. Newton’s Metaphysics.” In The Cambridge Companion to Newton, edited by I. B. Cohen and G. E. Smith, pp. 256–307. Cambridge, U.K.: Cambridge University Press, 2002.

Valluri, Sree Ram, Curtis Wilson, and William Harper. “Newton’s Apsidal Precession Theorem and Eccentric Orbits.” Journal for the History of Astronomy 28 (1997): 13–27.

Valluri, S. R., P. Yu, G. E. Smith, and P. A. Wiegart. “An Extension of Newton’s Apsidal Precession Theorem.” Monthly Notices of the Royal Astronomical Society 358 (2005): 1273–1284.

Whiteside, D. T. “The Prehistory of the Principia from 1664–1686.” Notes and Records, The Royal Society 45 (1991): 11–61.

Wilson, Curtis. “The Newtonian Achievement in Astronomy.” In Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part A: Tycho Brahe to Newton, edited by R. Taton and C. Wilson, pp. 233–274. Cambridge, U.K.: Cambridge University Press, 1989.

_____. Newton on the Moon’s Variation and Apsidal Motion: The Need for a Newer ‘New Analysis.’” In Isaac Newton’s Natural Philosophy, edited by J. Z. Buchwald and I. B. Cohen, pp. 139–188. Cambridge, MA: MIT Press, 2001.

_____. Newton and Celestial Mechanics.” In The Cambridge Companion to Newton, edited by I. B. Cohen and G. E. Smith, pp. 202–206. Cambridge, U.K.: Cambridge University Press, 2002.

George E. Smith

The Significance of Newton’s Alchemical Research In the original DSB (1974), I.B. Cohen wrote that it was it was “difficult to determine whether to consider Newton’s alchemy as an irrational vagary of an otherwise rational mind, or whether to give his hermeticism a significant role as a developmental force in his rational science” (DSB, vol.10, p. 82). Since the publication of these words, scholarly developments have substantially reduced the viability of Cohen’s first alternative. The topic of alchemy has yielded up much of its erstwhile mystery to scrutiny and it is clear that the subject was not only a reasonable field of endeavor in its day, but a veritable cause célèbre. Alchemy, or to use the largely synonymous early modern term, chymistry, included not only chrysopoeia (transmutation of base metals) but a host of more attainable pursuits, such as the making of medicines, dyes and pigments, alcoholic beverages, and colored glasses, and the metallurgical purification and reduction of ores. In short, the imposition of a modern distinction between alchemy and early chemistry is an anachronism.

Chymistry was also the source of diverse theories of material composition, including an important corpuscular theory of matter to which Newton and his older contemporary and acquaintance Robert Boyle were heirs. Having its roots in medieval alchemy, this corpuscular theory had no difficulty accommodating the transmutation of one metal into another by the replacement and rearrangement of particles at the micro-level. It is no mark of irrationality, then, that Newton and Boyle were committed seekers of the philosophers’s stone, and that such luminaries as John Locke and Gottfried W. Leibniz were all deeply interested in the aurific art. The age of gold was also the age of gold-making.

It is much harder to reply to Cohen’s second alternative. Although Newton’s alchemical work was certainly not an “irrational vagary,” it does not follow automatically that his chymistry contributed in any major way to Newton’s more famous scientific discoveries. Despite two major books by Betty Jo Teeter Dobbs on Newton’s alchemy that have appeared along with a number of articles devoted to the subject, as well as Richard Westfall’s magisterial biography, Never at Rest, the verdict is still out. Both Dobbs and Westfall were at various times inclined to see Newton’s alchemy as having contributed in a major way to his mature theory of gravitation, and more generally to his conviction that forces could operate at a distance. There is no direct evidence for this view in any of the documents submitted by Dobbs or Westfall for scrutiny, however, and on the few occasions when Newton did describe the causes of gravity in an explicitly alchemical context, he explained the falling of bodies by mechanical means, not as a result of force at a distance. This is particularly the case in Newton’s important early manuscript “Of Nature’s Obvious Laws & Processes in Vegetation” (Smithsonian Institution, Dibner MS. 1031B), where Newton postulated a material ether that forces bodies downward and is also responsible for chymical properties such as cohesion. In later works, such as Query 31 of the Opticks, Newton did import chymical powers in the form of a vis fermentativa whose ultimate source is the Flemish chymist Joan Baptista Van Helmont, but this “fermentative force” is quite distinct from gravitational attraction. Finally, it should be obvious that Newton had more immediate sources than alchemical literature to draw upon for the idea of immaterial forces acting on matter. In particular, he was the beneficiary of several centuries of research on the immaterial attraction exercised by magnets, beginning with Petrus Peregrinus in the thirteenth century and proceeding through the works of many seventeenth-century figures ranging from William Gilbert to Johannes Kepler. In a word, the idea that Newton derived his theory of universal gravitation from alchemy has become something of a canard.

But it does not follow from this, of course, that Newton’s chymistry had no connection with his more famous scientific endeavors, or that it wielded no influence upon them. One promising area lies in Newton’s early work on the analysis and synthesis of white light by means of prisms. From his earliest researches, Newton seems to have held the private conviction that light was composed of tiny corporeal bodies—corpuscles. Because Newton also viewed matter more generally as corpuscular, it is therefore not surprising that he recorded his fundamental optical discoveries alongside chymical phenomena and experiments in his early manuscripts, such as his Certain Philosophical Questions and the laboratory notebook now kept in Cambridge University Library under the shelf-mark Additional 3975.

Although Newton’s earliest efforts to break white light into its spectral colors by means of prisms seem to have had non-chymical sources, his decision to recombine those colors and hence recreate the light that he started with is highly suggestive of early modern chymistry. It is the largely chymical manuscript CU add. 3975 that contains the first record of Newton’s resynthesis of white light after his having analyzed it into its spectral colors, and the same codex contains Newton’s notes on Robert Boyle’s famous redintegration(resynthesis) of various materials from their components after they had been subjected to analysis. It is highly likely that the form of demonstration

employed by Newton, analysis followed by resynthesis, owed a significant debt to Boyle and to the tradition of alchemy as a whole, which had been expressly viewed as the “art of analysis and synthesis” since the beginning of the seventeenth century. Boyle’s important reintegration of saltpeter had received public notice when he published his Certain Physiological Essays (1661) and his Origine of Formes and Qualities(1666). Hence the resynthesis of compounds was a subject very much au courant in the scientific circles traveled by Newton at the very time when he was making his fundamental optical discoveries, and one that was sure to appeal to the young savant.

Newton’s Chymical Theory Whereas there was significant bleed-through from Newton’s chymistry to his other scientific endeavors, it is equally important to determine the nature of his chymistry as a whole, without judging it merely in relation to his physics. The chymical nachlass that Newton left unpublished (now being published on the Chymistry of Isaac Newton website) consists of about a million words of text that can be divided into four rough categories—synopses, transcriptions, and running commentaries on existing alchemical texts; cross-referencing and lexicographical tools such as Newton’s Index chemicus; laboratory notebooks such as CU add. 3975 and 3973; and treatises, or rather clusters of ideas arranged in the form of commonplace entries, such as “Of Nature’s Obvious Laws & Processes in Vegetation.” Of these four types of text, only the last provides a straightforward entry into Newton’s theory of chymistry. Hence the remaining remarks will focus on the main texts of this sort, namely “Of Nature’s Obvious Laws” and the hitherto unstudied Latin text also found in Smithsonian MS. Dibner 1031B that begins with the phrase “Humores minerales continuo decidunt” (“Mineral humidities continually fall down”). In these texts Newton presented a theory that the world is a vast living being, which continually inhales and exhales a subtle, vital, ethereal material. Within the earth this material provides the Urstoff from which minerals and metals are formed. On the surface of the earth, the same material accounts for the generation, growth, and sustenance of life.

It is clear that the material principle alluded to by Newton was his reworking of an idea derived from the sal nitrum theorists, a major school within early modern alchemy. The main figure associated with this movement was Michael Sendivogius, a Polish courtier, alchemist, and mining consultant in the employ of the Hapsburg emperor Rudolf II. Sendivogius’s Novum lumen chemicum(1604) and Tractatus de suphure(1616) argue that there is a volatile niter (also referred to as philosophical mercury) that circulates between the core of the earth and the sun. This fiery cosmic principle serves as the source of life on earth, and like Newton’s ether, it is involved in the subterranean generation of minerals and metals.

Curiously, Newton explicitly distanced himself from the sal nitrum theorists in his 1675 Hypothesis of Light. He presented a theory, however, that is otherwise remarkably similar to the one proposed in “Of Natures Obvious Laws.” After describing an aereal, volatile spirit that accounts for flame and vital activity in the Hypothesis, Newton said “I mean not the imaginary volatile saltpeter” [Turnbull, Correspondence of Isaac Newton, 1959, vol. 1, p. 365]. A. Rupert Hall has pointed out that Newton may have preferred the version of the sal nitrum theory found in Sendivogius’s work to contemporary English versions that had been influenced by Cartesianism. This could be the case, but a careful reading of Newton’s “Humores minerales,” the Latin text also found in Smithsonian MS. 1031B, reveals that Newton’s own theory of metallic generation was not entirely identical to that usually expressed by the sal nitrum school.

In its most common form, the volatile niter theory viewed subterranean processes in terms of the sublimation and condensation of mineral vapors. Within the earth, the volatile niter was supposed to combine with sulfur and various impurities to yield the metals by reiterate vaporization and condensation. If one consults Newton’s “Humores minerales,” however, it is immediately obvious that he introduced another process into the generation of metals, namely solution. Writing under the influence of the German alchemist Johannes Grasseus, Newton laid out an elaborate subterranean process. According to this theory, minerals are dissolved by underground acidities, which then analyze the minerals into their mercurial and sulfurous constituents and carry them downwards toward the center of the earth. The downwards-falling solution then encounters fumes that are rising upwards, and combines with them, which accounts for the generation of further metals from the initial dissolved minerals. The subterranean process of solution by naturally occurring acids therefore became an integral part of Newton’s theory, and the volatile niter of the sal nitrum theorists was nowhere openly mentioned by name. Nonetheless, “Humores minerales” concluded in a way quite similar to the niter theory’s insistence on a general, universal spirit. The text ended by saying “These two spirits [i.e. mercury and sulfur] above all wander over the earth and bestow life on animals and vegetables. And they make stones, salts, and so forth.”

As one can see from the texts in Smithsonian MS. Dibner 1031B, Newton used chymistry as the source for something like what physicists in the early twenty-first century call a “theory of everything,” namely a physical theory that unifies and accounts for all known natural phenomena. Although Newton’s alchemically-based theory did not belong to the realm of mathematical physics, it too tried to account for widely diverse phenomena, including organic life, the origin of heat and flame, the mechanical cause of gravitation, cohesion, the generation of metals and minerals, and so forth, by making an appeal to an ethereal medium. Perhaps because of the marvelous properties that Newton ascribed to the single ethereal medium behind such phenomena, some scholars have seen Newton’s interest in alchemy as arising above all from his religious sensibilities. In a qualified fashion this can be granted, because Newton’s science as a whole was undoubtedly conditioned by his deep religious convictions. Rather than seeing Newton’s chymistry as somehow more religiously oriented than his physics, however, one should view it as arising from the same desire to penetrate behind the appearances and to arrive at the most general possible explanation of reality. In the hands of Newton, both chymistry and physics were tools for arriving at fundamental truths about Nature and its operations.

SUPPLEMENTARBLIOGRAPHY

The totality of Newton’s chymical nachlass is being published on line in diplomatic and normalized versions with translations of the Latin as part of The Chymistry of Isaac Newton, edited by William R. Newton, available from http://www.dlib.indiana.edu/collections/newton/.

WORKS BY NEWTON

Dobbs, Betty Jo Teeter. The Foundations of Newton’s Alchemy: or, “The Hunting of the Greene Lyon. ” Cambridge, U.K.: Cambridge University Press, 1975. Several of Newton’s chymical writings have been edited and translated as appendices to this work and The Janus Faces of Genius.

—_____. The Janus Faces of Genius: The Role of Alchemy in Newton’s Thought. Cambridge, U.K.: Cambridge University Press, 1991.

McGuire, J. E., and Martin Tamny. Certain Philosophical Questions: Newton’s Trinity Notebook. Cambridge, U.K.: Cambridge University Press, 1983. Some chymical material is already found in Newton’s student notebook, Certain Philosophical Questions.

OTHER SOURCES

Dobbs, Betty Jo Teeter. “Newton Manuscripts at the Smithsonian Institution.” Isis68 (1977): 105–107.

_____. Newton’s Copy of Secrets Reveal’d and the Regimens of the Work.” Ambix26 (1979): 145–169.

_____. Newton’s Alchemy and his Theory of Matter.” Isis73 (1982): 511–528.

_____. Newton’s ‘Clavis’: New Evidence on its Dating and Significance.” Ambix 29 (1982): 190–202.

—_____. Review of Contemporary Newtonian Research, edited by Zev Bechler. Isis74 (1983): 609–610.

_____. Conceptual Problems in Newton’s Early Chemistry: A Preliminary Study.” In Religion, Science, and Worldview: Essays in Honor of Westfall, Richard S, edited by Margaret J. Osler and Paul L. Farber, pp. 3–32. Cambridge, U.K.: Cambridge University Press, 1985.

_____. Newton and Stocism.” The Southern Journal of Philosophy (Supplement)23 (1985): 109–123.

_____. Alchemistische Kosmogonie und arianiasche Theologie bei Isaac Newton.” Wolfenbütteler Forschungen 32 (1986): 137–155.

_____. Newton’s Alchemy and his ‘Active Principle’ of Gravitation.” In Newton’s Scientific and Philosophical Legacy, edited by Paul B. Scheuer and Guy Debrock, pp. 55–80. Dordrecht, Netherlands: Kluwer, 1988.

_____. Newton’s Commentary on The Emerald Tablet of Hermes Trimegistus: its Scientific and Theological Significance.” In Hermeticisim and the Renaissance: Intellectual History and the Occult in Early Modern Europe, edited by Ingrid Merkel and Allen G. Debus, pp. 182–191. Washington, D.C.: The Folger Shakespeare Library, 1988.

_____. Newton’s Rejection of a Mechanical Aether for Gravitation: Empirical Difficulties and Guiding Assumptions.” In Scrutinizing Science: empirical Studies of Scientific Change, edited by Arthur Donovan, Lary Laudan, and Rachel Laudan, pp. 69–83. Dordrecht, Netherlands: Kluwe, 1988.

—_____. Alchemical Death & Resurrection: The Significance of Alchemy in the Age of Newton. Washington, D.C.: Smithsonian Institution Libraries, 1990.

_____. Newton as Alchemist and Theologian.” In Standing on the Shoulders of Giants: A Longer View of Newton and Halley, edited by Norman J. W. Thrower, pp. 128–140. Berkeley: University of California Press, 1990.

_____. ‘The Unity of Truth’: An Integrated View of Newton’s Work.” In Action and Reaction: Proceedings of a Symposium to Commemorate the Tercentenary of Newton’s ‘Principia, ’ edited by Paul Theerman and Adele F. Seeff, pp. 105–122. Newark, NJ: University of Delaware Press, 1993. _____. Newton as Final Cause and First Mover.” Isis 85 (1994): 633–643.

_____. —, and Margaret C. Jacob. Newton and the Culture of Newtonianism. Atlantic Highlands, NJ: Humanities Press, 1995.

Figala, Karin. “Zwei Londoner Alchemisten um 1700: Sir Isaac Newton und Cleidophorus Mystagogus.” Physis18 (1976): 245–273.

_____. Newton as Alchemist.” History of Science15 (1977): 102–137.

_____. Die exakte Alchemie des von Isaac Newton.” Verhandlungen der Naturforschenden Gesellschaft in Basel94 (1984): 157–227.

_____. Newton’s Alchemy.” In The Cambridge Companion to Newton, edited by I. Bernard Cohen and George E. Smith, pp. 370–386. Cambridge, U.K.: Cambridge University Press, 2002.

_____. —, J. Harrison, and Ulrich Petzoldt. “De Scriptoribus Chemicis: Sources for the Establishment of Isaac Newton’s (Al)Chemical Library.” In The Investigation of Difficult Things, edited by P.M. Harman and A. E. Shapiro, pp. 135–179. Cambridge, U.K.: Cambridge University Press, 1992.

_____. —, and Ulrich Petzoldt. “Alchemy in the Newtonian Circle: Personal Acquaintances and the Problem of the Late Phase of Isaac Newton’s Alchemy.” In Renaissance and Revolution: Humanists, Scholars, Craftsmen, and Natural Philosophers in Early Modern Europe, edited by Judith V. Field and Frank A. J. L. James, pp. 173–192. Cambridge, U.K.: Cambridge University Press, 1993.

Golinski, Jan. “The Secret Life of an Alchemist.” In Let Newton Be!, edited by John Fauvel, pp. 147–167. Oxford, U.K.: Oxford University Press, 1988.

Hall, A. Rupert. Isaac Newton, Adventurer in Thought. Oxford, U.K.: Blackwell, 1992.

_____. Isaac Newton and the Aerial Nitre.” Notes and Records of the Royal Society of London52 (1998): 51–61.

_____. Pitfalls in the Editing of Newton’s Papers.” History of Science40 (2002): 407–424.

Lederer, Thomas. “Leben, Werk und Wirkung des Stralsunder Fachschriftstellers Johann Grasse (nach 1560–1618).” In Pommern in der Frühen Neuzeit, edited by Wilhelm Kuhlmann and Horst Langer, pp. 227–237. Tübingen, Germany: Max Niemeyer, 1994.

McGuire, James E. “Neoplatonism and Active Principles: Newton and the Corpus Hermeticum.” In Hermeticism and the Scientific Revolution, edited by Robert S. Westman and James E. McGuire, pp. 93–142. Los Angeles: Clark Memorial Library, University of California, 1977.

Newman, William R. “Newton’s Clavis as Starkey’s Key.” Isis78 (1987): 564–574. The “Clavis,” a work ascribed by Dobbs to Newton and published in The Foundations of Newton’s Alchemy, has subsequently been proven to be by George Starkey.

—_____. Gehennical Fire: The Lives of George Starkey, an American Alchemist in the Scientific Revolution. Cambridge, MA: Harvard University Press, 1994. revised ed. Chicago: University of Chicago Press, 2003.

_____. —, and Lawrence M. Principe. “Alchemy v. Chemistry: The Etymological Origins of a Historiographic Mistake.” Early Science and Medicine 3 (1998): 32–65.

_____. The Background to Newton’s Chymistry.” In The Cambridge Companion to Newton, edited by I. Bernard Cohen and George E. Smith, pp. 358–369. Cambridge, U.K.: Cambridge University Press, 2002.

—_____. Atoms and Alchemy: Chymistry and the Experimental Origins of the Scientific Revolution. Chicago: University of Chicago Press, 2006a. _____. From Alchemy to ‘Chymistry.’” In The Cambridge History of Science: Early Modern Science, vol. 3, pp. 497–517. Cambridge, U.K.: Cambridge University Press, 2006b.

Priesner, Claus, and Karin Figala. Alchemie: Lexikon einer hermetischen Wissenschaft. Munich, Germany: C. H. Beck, 1998.

Principe, Lawrence M. “The Alchemies of Robert Boyle and Isaac Newton: Alternate Approaches and Divergent Deployments.” In Rethinking the Scientific Revolution, edited by Margaret J. Osler, pp. 201–220. Cambridge, U.K.: Cambridge University Press, 2000.

_____. —, and William R. Newman. “Some Problems with the Historiography of Alchemy.” In Secrets of Nature: Astrology and Alchemy in Early Modern Europe, edited by William R. Newman and Anthony Grafton, pp. 385–431. Cambridge, MA: MIT Press, 2001.

Spargo, Peter E., and C. A. Pounds. “Newton’s ‘Derangement of the Intellect’: New Light on an Old Problem.” Notes and Records of the Royal Society of London34 (1979): 11–32.

_____. Newton’s Chemical Experiments: An Analysis in the Light of Modern Chemistry.” In Action and Reaction: Proceedings of a Symposium to Commemorate the Tercentenary of Newton’s ‘Principia, ’ edited by Paul Theerman and Adele F. Seeff, pp. 123–143. Newark, NJ: University of Delaware Press, 1993.

_____. Investigating the Site of Newton’s Laboratory in Trinity College, Cambridge.” South African Journal of Science101 (2005): 315–21.

Westfall, Richard S. “Isaac Newton’s Index Chemicus.” Ambix 22 (1975a): 174–185.

_____. The Role of Alchemy in Newton’s Career.” In Reason, Experiment and Mysticism in the Scientific Revolution, edited by M. L. Righini Bonelli and William R. Shea, pp. 189–232. New York: Science History Publications, 1975b.

_____. The Influence of Alchemy on Newton.” In Science, Pseudo-Science and Society, edited by Marsha P. Hanen, Margaret J. Osler, and Robert G. Weyant, pp. 145–169. Waterloo, Canada: Wilfred Laurier University Press, 1980a.

—_____. Never at Rest: A Biography of Isaac Newton. Cambridge, U.K.: Cambridge University Press, 1980b.

_____. Alchemy in Newton’s Library.” Ambix31 (1984): 97–101.

William Newman