The observations and theories of Copernicus, Tycho Brahe, Kepler, and Galileo, together with those of some of their contemporaries, represent the first stage of an intellectual upheaval that came to be called the Scientific Revolution, which continued through the seventeenth century and on into the early years of the eighteenth. Some historians today take issue with the concept of a “scientific revolution,” a term coined in 1939, but all agree that it was a period during which the cosmology of western Europe changed profoundly and the modern scientific tradition emerged.
Two different philosophies of science were formulated in the seventeenth century. One was the empirical, inductive method of Francis Bacon (1561-1626); the other was the theoretical, deductive approach of René Descartes (1596-1650).
According to Bacon, the new science should be based primarily on observation and experiment, and it should arrive at general laws only after a careful and thorough study of nature. Bacon never accepted the Copernican theory, which he called a “hypothesis,” and he criticized both Ptolemy and Copernicus for presenting nothing more than “calculations and predictions” rather than “philosophy… what is found in nature herself, and is actually and really true.”
Descartes sought to give physical laws the same certitude as those of mathematics, a program that he laid out in his Discourse on the Method of Reasoning Well and Seeking Truth in the Sciences Whereas in philosophy Descartes began with the existence of self(“Cogito ergo sum,” I am thinking, therefore I exist), in physics he started with the existence of matter, its extension in space, and its motion through space. That is, everything in nature can be reduced to matter in motion. Matter exists in discrete particles that collide with one another in their ceaseless motions, changing their individual velocities in the process, but with the total “quantity of motion” in the universe remaining constant. Descartes writes of the divine origin of this law in The Principles of Philosophy(1644). Speaking of God, he says, “In the beginning, in his omnipotence, he created matter, along with its motion and rest, and now, merely by his regular concurrence, he preserves the same amount of motion and rest in the material universe as he put there in the beginning.”
Descartes presented his method in Rules for the Direction of the Mind, completed in 1628 but not published until after his death, and in the Discourse on Method, published in 1637 along with appendices entitled “Optics,” “Geometry,” and “Meteorology.” He gave the final form of his three laws of nature in The Principles of Philosophy The first law, the principle of inertia, states that “Each and every thing, insofar as it can, always continues in the same state, and thus what is once in motion always continues to move.” The second law states that “all motion is in itself rectilinear… every piece of matter, considered in itself, always tends to continue moving, not in any oblique path but only in a straight line.” The third law is concerned with collisions: “If a body collides with another body that is stronger than itself, it loses none of its motion; but if it collides with a weaker body, it loses a quantity of motion equal to that which it imparts to the other body.”
The “Optics” presents Descartes's mechanistic theory of light, which he conceived of as a series of impulses propagated through the finely dispersed microparticles that fill the spaces between macroscopic bodies, leaving no intervening vacuum. This model gave him the right form for the law of refraction, but in his derivation he took the velocity of light to be greater in water than in air, which is not true.
The first correct derivation of the law of refraction appears to be the work of the Dutch mathematician Willebrord Snell (1580-1626), which was not published until after his death; it solved another problem that had eluded physicists since antiquity. The law, in its modern form, states that the ratio of the sines of the angles of incidence and refraction equals the ratio of the velocities of light in the two media.
The “Geometry” was inspired by what Descartes called the “true mathematics” of the ancient Greeks, particularly Pappus and Diophan-tus. Here he provided a geometric basis for algebraic operations, which to some extent had already been done by his predecessors as far back as al-Khwarizmi. The symbolic notation used by Descartes quickly produced great progress in algebra and other branches of mathematics. His work gave rise to the branch of mathematics now known as analytic geometry, which had been anticipated by Pierre Fermat (1601-65). Fer-mat, inspired by Diophantus and Apollonius, was also one of the founders of modern number theory and probability theory.
Descartes's “Meteorology” includes his theory of the rainbow, in which he used the laws of reflection and refraction to obtain the correct values of the angles at which the primary and secondary bows appear. He attempted to give a qualitative explanation of the colors of the rainbow, but this was based on his erroneous notion that light travels faster in water than in air.
Chapters 8 through 12 of Descartes's Le monde, ou Traité de la lumière, present his mechanistic cosmology, based on his theory of matter and laws of motion. This hypothetical “new world” that he describes consisted of an indefinite number of contiguous vortices, each with a star like our sun at the center of a planetary system, all carried around by the motion of the particles of the three types of matter that he believed filled all of space.
Descartes's vortex theory was generally accepted at first, but the researches of Christiaan Huygens (1629-95) showed conclusively that it was completely incorrect. Huygens was led to his rejection of the vortex theory by his studies of dynamics. In one of his studies he considered a situation in which a lead ball is attached to a string held by a man standing at the center of a rotating platform. When the platform rotates the man feels an outward or centrifugal force in the string attached to the ball, which in turn experiences an inward or centripetal force due to the string. Huygens found that the centripetal force on the ball was directly proportional to the mass of the ball and the square of its velocity and inversely proportional to the radius of its circular path, thus establishing the basis of dynamics for circular motion. This and his researches on the laws of collisions were what led Huygens to conclude that the Cartesian cosmology was in error. As he said in 1693, he could find “almost nothing I can approve as true in all the physics and metaphysics” of Descartes.
Descartes's Aristotelian notion that a vacuum was impossible was also shown to be incorrect by several of his contemporaries, beginning with Evangelista Torricelli (1608-47) and Blaise Pascal (1623-62). Torri-celli's invention of the barometer in 1643 led him to conclude that the closed space above the mercury column represented at least a partial vacuum, and that the difference in the height of the two columns in the U-tube was a measure of the weight of a column of air extending to the top of the atmosphere. Pascal had a barometer taken to the top of the Puy de Dôme, a peak in central France, and it was observed that the difference in height of the two columns was less than at sea level, verifying Torricelli's conclusions. The results of this experiment led Pascal to urge all disciples of Aristotle to see if the writings of their master could explain the results. “Otherwise,” he wrote, “let them recognize that experiments are the real masters that we should follow in physics; that the experiment done in the mountains overturns the universal belief that nature abhors a vacuum.”
The German engineer Otto von Guericke (1602-1686) discovered that it was possible to pump air as if it were water, allowing him to produce a vacuum mechanically. In a famous experiment at Magdeburg in 1657, he pumped the air out of a spherical cavity made by fitting together two copper hemispheres, and showed that the resulting differential pressure was so great that not even two teams of horses pulling in opposite directions could force the two halves of the sphere apart.
Guericke's demonstration led the Irish chemist Robert Boyle (1627-1691) to make his own vacuum pump, using a design by the English physicist Robert Hooke (1635-1703). Boyle used his vacuum pump to do research on pneumatics, which he published in 1660 under the title New Experiments Physico-Mechanicall, Touching the Spring of Air and Its Effects His conclusions were that a vacuum can be produced, or at least a partial one; that sound does not propagate in a vacuum; that air is necessary for life or a flame; and that air is elastic. In an appendix to the second edition of this work, published in 1662, he established the relationship now known as Boyle's law, that the pressure exerted by a gas is inversely proportional to its volume.
Boyle was influenced by both Francis Bacon's empiricism and Descartes's mechanistic view of nature. He was also influenced by the natural philosophy of Epicurus, which was revived by Pierre Gassendi (1592-1655), a French Catholic priest who in 1647 published a work in which he attempted to reconcile the atomic theory with Christian doctrine. This led Boyle to adopt a divinely ordained corpuscular version of mechanism, which he described in his treatise Some Thoughts About the Excellence and Grounds of the Mechanical Philosophy, published in 1670.
The culmination of the scientific revolution came with the career of Isaac Newton (1642-1727), whose supreme genius made him the central figure in the emergence of modern science.
Newton was born on 25 December 1642, the same year that Galileo died. His birthplace was the manor house of Woolsthorpe in Lincolnshire, England. His father, an illiterate farmer, had died three months before Isaac was born, and his mother remarried three years later, though she was widowed again after eight years. When Newton was twelve he was enrolled in the grammar school at the nearby village of Grantham, and he studied there until he was eighteen. His maternal uncle, a Cambridge graduate, sensed that his nephew was gifted and persuaded Isaac's mother to send the boy to Cambridge, where he was enrolled at Trinity College in June 1661.
At Cambridge Newton was introduced to both Aristotelian science and cosmology as well as the new physics, astronomy, and mathematics of Copernicus, Kepler, Galileo, Fermat, Descartes, Huygens, and Boyle. In 1663 he began studying under Isaac Barrow (1630-77), the newly appointed Lucasian professor of mathematics and natural philosophy. Barrow edited the works of Euclid, Archimedes, and Apollonius and published his own works on geometry and optics, with the assistance of Newton.
By Newton's own testimony he began his researches in mathematics and physics late in 1664, shortly before an outbreak of plague closed the university at Cambridge and forced him to return home. During the next two years, his anni mirabiles, he says, he discovered his laws of universal gravitation and motion as well as the concepts of centripetal force and acceleration.
This indicates that Newton had derived the law for centripetal force and acceleration by 1666, some seven years before Huygens, though he did not publish it at the time. He applied the law to compute the centripetal acceleration at the earth's surface caused by its diurnal rotation, finding that it was less than the acceleration due to gravity by a factor of 250, thus settling the old question of why objects are not flung off the planet by its rotation. He computed the centripetal force necessary to keep the moon in orbit, comparing it to the acceleration due to gravity at the earth's surface, and found that they were inversely proportional to the squares of their distances from the center of the earth. Then, using Kepler's third law of planetary motion together with the law of centripetal acceleration, he verified the inverse square law of gravitation for the solar system. At the same time he laid the foundations for the calculus and formulated his theory for the dispersion of white light into its component colors. “All this was in the two plague years 1665 and 1666,” he wrote, “for in those years I was in the prime of my age for invention & minded Mathematicks & Philosophy more than at any time since.”
When the plague subsided Newton returned to Cambridge, arriving in the spring of 1667. Two years later he succeeded Barrow as Lucasian professor of mathematics and natural philosophy, a position he was to hold for nearly thirty years.
During the first few years after he took up his professorship Newton devoted much of his time to research in optics and mathematics. He continued his experiments on light, examining its refraction in prisms and thin glass plates as well as working out the details of his theory of colors. He also carried on with his chemical experiments; like many of his contemporaries, he was still influenced by the old notions of alchemy.
Newton's silence allowed Robert Hooke (1635-1703) to claim that he was the first to discover the inverse-square law of gravitational force. In November 1662 Hooke had been appointed as the first curator of experiments at the newly founded Royal Society in London, a position he held until his death in 1703. Hooke made many important discoveries in mechanics, optics, astronomy, technology, chemistry, and geology. He is remembered today principally for the relation known as Hooke's law, which states that the force necessary to stretch a spring is proportional to the extension of the spring, a concept that can be applied to study any simple harmonic motion.
Meanwhile, Newton continued his researches on light, and he succeeded in making a reflecting telescope that was a significant improvement on any of the refractors then in use. News of his invention leaked out and he was urged to exhibit it at the Royal Society in London, which was just then beginning to hold its formal weekly meetings. The exhibit was so successful that Newton was proposed for membership in the Royal Society and on 11 January 1672 he was elected as a fellow.
As part of his obligations as a fellow, Newton wrote a paper on his optical experiments, which he submitted on 28 February 1672, to be read at a meeting of the society. The paper, subsequently published in the Philosophical Transactions of the Royal Society,described his discovery that sunlight is composed of a continuous spectrum of colors, which can be dispersed by passing light through a refracting medium such as a glass prism. He found that the “rays which make blue are refracted more than the red,” and he concluded that sunlight is a mixture of light rays, some of which are refracted more than others. Furthermore, once sunlight is dispersed into its component colors it cannot be further decomposed. This meant that the colors seen on refraction are inherent in the light itself and are not imparted to it by the refracting medium.
The procedures described in the paper were characteristic of Newton's favored approach to any scientific investigation. Later, in a controversy arising out of his first paper, Newton described his scientific method:
For the best and safest method of philosophizing seems to be, first to enquire diligently into the properties of things, and to establish these properties by experiment, and then to proceed more slowly to hypotheses for the explanation of them. For hypotheses should be employed only in explaining the properties of things, but not assumed in determining them, unless so far as they may furnish experiments.
Ironically, the paper was widely criticized by Newton's contemporaries for just the contrary reason: that it did not confirm or deny any general philosophy of nature; the mechanists objected that it was impossible to explain his findings on the basis of any mechanical principles. Others insisted that Newton's experimental findings were false, since they themselves could not find the phenomena he had reported. Newton replied patiently to each of these criticisms in turn, but after a time he began to regret ever having presented his work in public. To make matters worse, Hooke began to claim that Newton's telescope was far inferior to one he himself had made.
For these and other reasons, early in 1673, Newton offered his resignation to the Royal Society. The secretary, Henry Oldenburg, refused to accept it and persuaded him to remain. But in 1676, after a public attack by Hooke, Newton broke off almost all association with the Royal Society. That same year Hooke became secretary of the society and wrote a conciliatory letter in which he expressed his admiration for Newton. Referring to Newton's theory of colors, Hooke said that he was “extremely well pleased to see those notions promoted and improved which I long since began, but had not time to compleat.”
Newton replied in an equally conciliatory tone, referring to Descartes's work on optics. “What Descartes did was a good step. You have added much several ways, and especially in taking the colours of thin plates into philosophical consideration. If I have seen further than Descartes, it is by standing on the sholders [sic] of Giants.”
Despite these friendly sentiments, the two were never completely reconciled, and Newton maintained his silence. Nevertheless, they continued to communicate with each other, a correspondence that was to lead again and again to controversy, the bitterest dispute arising from Hooke's claim that he had discovered the inverse-square law of gravitation before Newton.
By 1684 others beside Hooke and Newton were convinced that the gravitational force was responsible for holding the planets in their orbits, and that this force varied with the inverse square of their distance from the sun. Among them were the astronomer Edmund Halley (1656-1742), a good friend of Newton's and a fellow member of the Royal Society. Halley made a special trip to Cambridge in August 1684 to ask Newton “what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it.” Newton replied immediately that it would be an ellipse, but he could not find the calculation, which he had done seven or eight years before. And so he was forced to rework the problem, after which he sent the solution to Halley that November.
By then Newton's interest in the problem had revived, and he developed enough material to give a course of nine lectures in the fall term at Cambridge, under the title of De Motu Corporum (The Motion of Bodies). When Halley read the manuscript of De Motu he realized its immense importance, and he obtained Newton's promise to send it to the Royal Society for publication. Newton began preparing the manuscript for publication in December 1684 and sent the first book of the work to the Royal Society on 28 April 1686.
On May 22 Halley wrote to Newton saying that the society had entrusted him with the responsibility for having the manuscript printed. But he added that Hooke, having read the manuscript, claimed that it was he who had discovered the inverse-square nature of the gravitational force and thought that Newton should acknowledge this in the preface. Newton was very much disturbed by this, and in his reply to Halley he went to great lengths to show that he had discovered the inverse-square law of gravitation and that Hooke had not contributed anything of consequence.
The first edition of Newton's work was published in midsummer 1687 at Halley's expense, since the Royal Society had found itself financially unable to fund it. Newton entitled his work Philosophicae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy); it is referred to more simply as the Principia The Principia begins with an ode dedicated to Newton by Halley. This is followed by a preface in which Newton outlines the scope and philosophy of his work:
Our present work sets forth mathematical principles of natural philosophy. For the basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions, and then to demonstrate the other phenomena from these forces…. Then the motions of the planets, the comets, the moon, and the sea are deduced from these forces by propositions that are also mathematical. If only we could derive the other phenomena of nature from mechanical principles by the same kind of reasoning!
The introduction begins with a series of eight definitions, of which the first five are fundamental to Newtonian dynamics. The first effectively defines “quantity of matter,” or mass, as being proportional to the weight density times volume. The second defines “quantity of motion,” subsequently to be called “momentum,” as mass times velocity. In the third definition Newton says that the “inherent force of matter,” or inertia, “is the power of resisting by which every body, so far as it is able, perseveres in its state either of rest or of moving uniformly straight forward.” The fourth states, “Impressed force is the action exerted upon a body to change its state either of resting or of uniformly moving straight forward.” The fifth through eighth define centripetal force as that by which bodies “are impelled, or in any way tend, toward some point as to a center.” As an example Newton offers the gravitational force of the sun, which keeps the planets in orbit.
As regards the gravity of the earth, he gives the example of a lead ball, projected from the top of a mountain with a given velocity and in a direction parallel to the horizon. If the initial velocity is made larger and larger, he says, the ball will go farther and farther before it hits the ground, and may go into orbit around the earth or even escape into outer space.
The definitions are followed by a “Scholium,” a lengthy comment in which Newton explains his notions of absolute and relative time, space, place, and motion. These essentially define the classical laws of relativity, which in the early twentieth century would be superceded by Einstein's theories of special and general relativity.
An illustration from Newton's Principia showing a projectile in orbit around the earth.
Next come the axioms, now known as Newton's laws of motion, three in number, each accompanied by an explanation and followed by corollaries:
Law 1: Every body perseveres in its state of being at rest, or of moving uniformly forward, except insofar as it is compelled to change its state of motion by forces impressed…. Law 2: A change of motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed…. Law 3: To every action there is always an opposite and equal reaction; in other words, the action of two bodies upon each other are always equal, and always opposite in direction.
The first law is the principal of inertia, which is actually a special case of the second law when the net force is zero. The form used today for the second law is that the force F acting on a body is equal to the time rate of change of the momentum p, where pequals the mass m times the velocity v; if the mass is constant, then F = ma, a being the acceleration, the time rate of change of the velocity. The third law says that when two bodies interact the forces they exert on each other are equal in magnitude and opposite in direction.
Book 1 of the Principia is entitled “The Motion of Bodies.” This begins with an analysis of motion in general, essentially using the calculus. First Newton analyzed the relations between orbits and central forces of various kinds. From this he was able to show that if and only if the force of attraction varies as the inverse square of the distance from the center of force, then the orbit is an ellipse, with the center of attraction at one focal point, thus proving Kepler's second law of motion. Elsewhere in Book 1 he proves Kepler's first and third laws. He also shows that, for inverse-square forces, the net force at a point within a spherical shell is zero, while the force outside a solid sphere is the same as if all the mass were concentrated at its center, so that in dealing with the solar system the sun and planets can be treated as point masses.
Book 2 is also entitled “The Motion of Bodies;” for the most part it deals with forces of resistance to motion in various type of fluids. One of Newton's purposes in this analysis was to see what effect the hypothetical aether in Descartes's cosmology would have on the motion of the planets. His studies showed that the Cartesian vortex theory was completely erroneous, for it ran counter to the laws of motion in resisting media that he'd established earlier in Book 2.
The third and final book of the Principia is entitled “The System of the World” and begins with three “Rules for the Study of Natural Philosophy.” After this comes a section headed “Phenomena,” in which he treats six of these, followed by forty-two “Propositions,” each accompanied by a “Theorem” and sometimes followed by a “Scholium.” This is in turn followed by a “General Scholium” and a concluding section entitled “The System of the World.”
The six phenomena concern the motion of the planets and the earth's moon, along with observations about Kepler's second and third laws of planetary motion. He concludes that the planets “by radii drawn to the center…, describe areas proportional to the times, and their periodic times—the fixed stars being at rest—are as the 3/2; powers of their distances from that center.”
The first six propositions are arguments to show that the inverse-square gravitational force explains the motion of the planets orbiting the sun, the satellites of Jupiter, and the earth's moon, as well as the local gravity on the earth itself. The seventh proposition states Newton's law of universal gravitation: “Gravity exists in all bodies universally and is proportional to the quantity of matter in each.”
Proposition 13 states Kepler's first and second laws of planetary motion: “The planets move in ellipses that have a focus in the center of the sun, and by radii drawn to that center they describe areas proportional to the times.”
Proposition 18 says, “The axes of the planets are smaller than the diameters that are drawn perpendicular to the axes”—that is, the planets are oblate spheres. Newton correctly attributed this effect to the centrifugal forces arising from the axial rotation of the planets, so that the earth, for example, is flattened at the poles and bulges around the equator.
Proposition 24 presents Newton's theory of tidal action, that “the ebb and flow of the sea arises from the actions of the sun and moon,” finally solving a problem that dated back to the time of Aristotle.
Proposition 39 is “To find the precession of the equinoxes,” including the gravitational forces of both the sun and the moon on the earth. Newton correctly computed that “the precession of the equinoxes is more or less 5 0 seconds [of arc] annually,” thus solving another problem that had preoccupied astronomers for some two thousand years.
Lemma 4 states, “The comets are higher than the moon, and move in the planetary regions.” In the lemmas and propositions that follow, Newton discusses the motion of comets, showing that they move in elliptical orbits around the sun, thus reappearing periodically, as did the one known as Halley's comet, which had been observed in 1682 after disappearing seventy-five years before. He also speculated on the nature of comets, saying, as had Kepler, that the tail of a comet represents vaporization from the comet's head as it approaches the sun.
This is followed by a “General Scholium,” in which Newton says that mechanism alone cannot explain the universe, whose harmonious order indicates to him the design of a Supreme Being. “This most elegant system of the sun, planets, and comets could not have arisen without the design and dominion of an intelligent and powerful being.”
A second edition of the Principia was published in 1713 and a third in 1726, in both cases with a preface written by Newton. Meanwhile, in 1704 Newton had published his researches on light, much of which had been done early in his career. Unlike thePrincipia, which was in Latin, the first edition of his new work was in English, entitled Opticks, or a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light The first Latin edition appeared in 1706, and subsequent English editions appeared in 1717-18, 1721, and 1730; the last, which came out three years after Newton's death, bore a note stating that it was “corrected by the author's own hand, and left before his death, with his bookseller.”
Like the Principia, the Opticks is divided into three books. At the very beginning of Book I Newton reveals the purpose he had in mind when composing his work. “My design in this Book,” he writes, “is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiment.”
The topics dealt with in Book I include the laws of reflection and refraction, the formation of images, and the dispersion of light into its component colors by a glass prism. Other topics include the properties of lenses and Newton's reflecting telescope, the optics of human vision, the theory of the rainbow, and an exhaustive study of color. Newton's proof of the law of refraction is based on the erroneous notion that light travels more rapidly in glass than in air, the same error Descartes had made. This error stems from the fact that both of them thought that light was corpuscular in nature.
Newton's corpuscular view of light stemmed from his acceptance of the atomic theory. He writes of his admiration for “the oldest and most celebrated Philosophers of Greece… who made a Vacuum, and Atoms, and the Gravity of Atoms, the first Principles of their Philosophy.” Later on, he says, “All these things being consider'd, it seems to me that God in the Beginning formed Matter in solid, hard, impenetrable, moveable Particles, of such Sizes and Figures, and with such other Properties and in such Proportions to Space, as much conduced to the End for which he had form'd them.”
Book II begins with a section entitled “Observations Concerning the Reflexions, Refractions, and Colours of Thin Transparent Bodies.” The effects he studied here are now known as interference phenomena; Newton's observations are the first evidence for the wavelike nature of light.
In Book II Newton also comments on the work of the Danish astronomer Olaus Roemer (1644-1710), who in 1676 measured the velocity of light by observing the time delays in successive eclipses of the Jovian moon Io as Jupiter receded from the earth. Roemer's value for the velocity of light was about a fourth lower than the currently accepted one of slightly less than 300,000 kilometers per second, but it was nevertheless the first measurement to give an order of magnitude estimation of one of the fundamental constants of nature. Roemer computed that light would take eleven minutes to travel from the sun to the earth, as compared to the correct value of eight minutes and twenty seconds. Newton seems to have made a better estimate of the speed of light than Roemer, for in Book II of the Opticks he says, “Light is propagated from luminous Bodies in time, and spends about seven or eight Minutes of an Hour in passing from the Sun to the Earth.”
The opening section of Book III deals with Newton's experiments on diffraction. The remainder of the book consists of a number of hypotheses, not only on light, but on a wide variety of topics in physics and philosophy. The first edition of the Opticks had sixteen of these “Queries,” the second twenty-three, the third and fourth thirty-one. It would seem that Newton, in the twilight of his career, was bringing out into the open some of his previously undisclosed speculations, his heritage for those who would follow him in the study of nature.
Meanwhile, Newton had been involved in a dispute with the great German mathematician and philosopher Gottfried Wilhelm Leibniz, the point of contention being which of them had been the first to develop the calculus. According to his own account, Newton first conceived the idea of his “method of fluxions” around 1665-66, although he did not publish it until 1687, when he used it in the Principia He first published his work on the calculus independently in a treatise that came out in 1711. Leibniz began to develop the general methods of the calculus in 1675, though he did not publish his work until 1684. The version of calculus formulated by Leibniz, whose notation was much like that used today, caught on more rapidly than that of Newton, particularly on the Continent. Newton's bitterness over the dispute was such that in the third edition of the Principia he deleted all reference to Leibniz, who until the end of his days continued to accuse his adversary of plagiarism.
Aside from his work in science, Newton also devoted much of his time to studies in alchemy, prophecy, theology, mythology, chronology, and history. His most important nonscientific work is Observations upon the Prophecies of Daniel, and the Apocalypse of St. John, which is considered to be a possible key to the method of his alchemical studies, as evidenced by such notions as his analogy between the “four metals” of alchemy and the four beasts of the Apocalypse.
Newton died in London on 20 March 1727, four days after presiding over a meeting of the Royal Society, of which he had been president since 1703. His body lay in state until April 4, when he was buried with great pomp in Westminster Abbey. Voltaire, writing of Newton's funeral, noted, “He lived honored by his compatriots and was buried like a king who had done good to his subjects.”
In the last days of his life Newton had remarked, “I do not know what I may appear to the world; but to myself I seem to have been only like a boy, playing on the seashore, and diverting myself, in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”