Theory and Practice in Newton’s Alchemical Experimentation

Isaac Newton’s laboratory notebooks describe decades of experimentation in alchemy, extending from the late 1660s or early 1670s up until his departure for the Royal Mint in the 1690s. As they stand, however, the highly detailed experiments are extremely hard to decipher. Newton gives few clues about their purpose and the idiosyncratic character of the experiments when compared to those of other alchemists makes it difficult to interpret them in terms of protocols from contemporary chymistry. At other places in his extensive chymical corpus, however, Newton presents theoretical ruminations that may provide the key to his experimentation. This is the first article to attempt a detailed comparison of Newton’s alchemical theory with his laboratory practice.

Newton’s Laws of Motion

An obstacle to reading the Principia is presuming that the Laws of Motion attributed to Newton in physics textbooks, and the concept of force in them, are the same as those in the book; they are not. This chapter provides an account of his Laws and his conception of force as his contemporaries would have understood them. It does so first by giving the historical background to them in works by Descartes, Christiaan Huygens, John Wallis, and Christopher Wren; and then by reviewing the history of Newton’s own reformulations of them not just in the sequence of manuscripts leading up to the first edition, but extending even to the second edition. In the Principia the Laws serve as the basis for deriving conclusions about forces governing the motions in our planetary system from the motions of the bodies within it “among themselves.” Crucial to their doing so are their six Corollaries, some of them initially formulated as Laws. The history of their development too is covered in parallel with that of the Laws, emphasizing their crucial role in licensing those inferences regarding forces from the observed motions.

The Principia, from Conception to Publication

We lack a complete manuscript record covering the development of the Principia from the time Newton took the initial steps toward it with the short tract De motu corporum in gyrum sent to Halley in November 1684 until Halley received the final parts of the manuscript for the first edition in March 1687. What we have, beside occasional correspondence, are fragmentary manuscripts plus one complete manuscript composed in the spring and summer of 1685, De Motu Corporum, Liber Secundus—the forerunner in “popular” style of Book 3. The many deletions and revisions Newton made to these manuscripts and the evolution of his terminology from one of them to the next allow a reconstruction of the sequence of both them and the steps he went through over this nearly two-and-a-half-year period. This chapter presents such a reconstruction, describing each manuscript that we have from the period in sequence along with pertinent correspondence, with emphasis on the steps displayed in each that Newton took in his progress toward the first edition.

Newton and Chronology

This article details Isaac Newton’s studies of chronology, which resulted in the posthumously published Chronology of Ancient Kingdoms Amended. In the Chronology, Newton employed methods from genealogy and astronomy to provide a much-contracted history of the Mediterranean world that fitted into the time allowed for by Scripture. Originally a single treatise, “Theologiae Gentilis Origines Philosophicae,” discussing the Egyptian origins of star worship and how all ancient mythology could be mapped onto Noah and his progeny, it soon evolved into a multi-chapter work, the “Originals,” which included chapters like “The Original of Religions” and “The Original of Monarchies.” Together with chapters on the history of the monarchies that reigned over Babylon during the Jewish Exile, the “Originals” became the Chronology; but its editorial history demonstrates how Newton’s interest in chronology was motivated by his desire to correctly interpret the apocalyptic prophecies in Scripture.

Leibniz and Newton as Critics of Descartes

Leibniz and Newton famously disagreed on many philosophical and mathematical topics. Indeed, their disagreements are legion in the eighteenth century and beyond. But underlying their disputes, there are some important and illuminating similarities in their reactions to Cartesian natural philosophy. The Leibniz-Clarke correspondence, along with certain interpretations of the vis viva dispute, have obscured these similarities, which are an important aspect of our understanding of Newton’s work.

Experiments in the Principia

Newton carried out four groundbreaking experiments in conjunction with the Principia and proposed a fifth. This chapter reviews his reasons for doing them, their design, and what they achieved. The four include a two-pendulum experiment early in 1685 to establish that the action of gravitational forces on a body is always proportional to its mass and hence that all bodies at any point respond to a gravitational force in the same way. In that same year he conducted a ballistic pendulum experiment to establish that this third law of motion holds for impact of spheres of a wide range of elastic responses, in the process identifying what became known as the coefficient of restitution. He carried out two sets of experiments measuring fluid resistance forces on spheres, the less than successful first relying on pendulum decay and then, for the second edition, vertical-fall. All five experiments were designed to “put the question to nature” in the sense that the three laws of motion enable their results to yield theory-mediated answers to theretofore open questions about forces—and thus parallel the answers to questions about celestial forces drawn from planetary motions that form the core of the Principia.

Newton in the Pool Hall: Subtleties of the Third Law

In order to apply the Third Law of Motion to widely separated celestial bodies, Newton must confront the experimental behaviors of colliding billiard balls, despite the fact that such objects otherwise play little role within the Principia’s formal developments. This challenge forces Newton to confront the fraught question of the sources of their elastic rebound and to postulate implausible “hard atoms” as a result. Leibniz’s surprising opinions on this same topic are presented by way of contrast.

The Quiet Scientific Revolution: Problem-Solving and the Eighteenth-Century Origins of “Newtonian” Mechanics

A narrative is proposed for eighteenth-century origins of “Newtonian” mechanics, according to which there are two relevant streams of development. One was the popularization of Newtonian natural philosophy, particularly in France in connection with the philosophe movement and the Enlightenment. This movement was inspired primarily by the example of Newton’s Opticks and embraced induction from observation and experiment. Newton’s Principia (1687), on the other hand, and its mathematical treatment of forces and motion, was exceedingly difficult. Solving novel problems in mechanics not addressed in the Principia required the kind of training possessed by a select group of mathematicians, most of whom were already engaged in a program of mathematical mechanics and did not identify as Newtonians nor took Principia as their starting point. The loudly celebrated, popular Newtonianism was lacking a program in mechanics until the end of the eighteenth century, when it subsumed, ironically, the mechanics of the non-Newtonians.

Newton’s Scientific Method

One central feature of Newton’s methodology is the use of theory-mediated measurements to make empirical phenomena carry information about causal dependencies. Accurate measurements of theoretical parameters by phenomena is a conception of empirical success that goes beyond the restriction of empirical success to accurate prediction of phenomena in the hypothetico-deductive model of scientific inference. This is informed by Newton’s account of provisional acceptance of propositions gathered from phenomena in his Fourth Rule of reasoning. Another feature is to follow up the discovery of forces of nature by applying those forces to additional phenomena. This is illustrated by the sequence of refinements of the model for solar system motions as more and more dependencies corresponding to Newtonian interactions were taken into account. Given that his theory would recover these Newtonian causal dependencies, Einstein’s Mercury perihelion result made his theory of gravity more empirically successful than Newton’s.

Newton’s Mathematics

This article introduces a number of critical features of Newton’s mathematics with specific reference to his views on controversial contemporary topics, including mathematical notations, infinitesimals, and the relationship between geometry and algebra. It pays attention to Newton’s lengthy discussion of the solution of the “inverse problem” by transformation of areas, its partial publication in De Quadratura curvarum (1704), and the Continental influence this treatise exerted. The substantial gap between Newton’s unpublished contributions and the published record is introduced as essential background for the priority quarrel and for the reception of Newton’s calculus generally. The paper argues that Newton’s uncommon (for the period) views on algebra and his cavalier attitude towards symbolization were major factors in shaping Newton’s fluxional calculus at variance with Leibnizian infinitesimal calculus.