Newton, Sir Isaac

I INTRODUCTION

Newton, Sir Isaac (1642-1727), English physicist, mathematician, and natural philosopher, considered one of the most important scientists of all time. Newton formulated laws of universal gravitation and motion—laws that explain how objects move on Earth as well as through the heavens (see Mechanics). He established the modern study of optics—or the behavior of light—and built the first reflecting telescope. His mathematical insights led him to invent the area of mathematics called calculus (which German mathematician Gottfried Wilhelm Leibniz also developed independently). Newton stated his ideas in several published works, two of which, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy, 1687) and Opticks (1704), are considered among the greatest scientific works ever produced. Newton’s revolutionary contributions explained the workings of a large part of the physical world in mathematical terms, and they suggested that science may provide explanations for other phenomena as well.

Newton took known facts and formed mathematical theories to explain them. He used his mathematical theories to predict the behavior of objects in different circumstances and then compared his predictions with what he observed in experiments. Finally, Newton used his results to check—and if need be, modify—his theories (see Deduction). He was able to unite the explanation of physical properties with the means of prediction. Newton began with the laws of motion and gravitation he observed in nature, then used these laws to convert physics from a mere science of explanation into a general mathematical system with rules and laws. His experiments explained the phenomena of light and color and anticipated modern developments in light theory. In addition, his invention of calculus gave science one of its most versatile and powerful tools.

II EARLY LIFE AND EDUCATION

Newton was born in Woolsthorpe, Lincolnshire, in England. Newton’s father died before his birth. When he was three years old, his mother remarried, and his maternal grandmother then took over his upbringing. He began his schooling in neighboring towns, and at age ten was sent to the grammar school at nearby Grantham. While at school he lived at the house of a pharmacist named Clark, from whom he may have acquired his lifelong interest in chemical operations. The young Newton seems to have been a quiet boy who was skilled with his hands. He made sundials, model windmills, a water clock, a mechanical carriage, and flew kites with lanterns attached to their tails. However, he was (as he recounted late in his life) very inattentive at school.

In 1656 Newton’s mother, on the death of her second husband, returned to Woolsthorpe and took her son out of school in the hope of making him a farmer. Newton showed no talent for farming, however, and according to legend he once was found under a hedge deep in study when he should have been in the market at Grantham. Fortunately, Newton’s former teacher at Grantham recognized the boy’s intellectual gifts and eventually persuaded Newton’s mother to allow him to prepare for entrance to University of Cambridge. In June 1661 Trinity College at Cambridge admitted Newton as a subsizar (a student required to perform various domestic services). His studies included arithmetic, geometry, trigonometry, and, later, astronomy and optics. He probably received much inspiration at Trinity from distinguished mathematician and theologian Isaac Barrow, who was a professor of mathematics at the college. Barrow recognized Newton’s genius and did all he could to cultivate it. Newton earned his bachelor’s degree in January 1665.

III EARLY SCIENTIFIC IDEAS

When an outbreak of bubonic plague in 1665 temporarily shut down University of Cambridge, Newton returned to Woolsthorpe, where he remained for nearly two years. This period was an intellectually rich one for Newton. During this time, he did much scientific work in the subjects he would spend his life exploring: motion, optics, and mathematics.

At this point, according to his own account, Newton had made great progress in what he called his mathematical “method of fluxions” (which today we call calculus). He also recorded his first thoughts on gravitation, inspired (according to legend) by observing the fall of an apple in an orchard. According to a report of a conversation with Newton in his old age, he said he was trying to determine what type of force could hold the Moon in its path around Earth. The fall of an apple led him to think that the attractive gravitational force acting on the apple might be the same force acting on the Moon. Newton believed that this force, although weakened by distance, held the Moon in its orbit.

Newton devised a numerical equation to verify his ideas about gravity. The equation is called the inverse square law of attraction, and it states that the force of gravity (an object’s pull on another object) is related to the inverse square of the distance between the two objects (that is, the number 1 divided by the distance between the two objects times itself). Newton believed this law should apply to the Sun and the planets as well. He did not pursue the problem of the falling apple at the time, because calculating the combined attraction of the whole Earth on a small body near its surface seemed too difficult. He reintroduced these early thoughts years later in his more thorough work, the Principia.

Newton also began to investigate the nature of light. White light, according to the view of his time, was uniform, or homogeneous, in content. Newton’s first experiments with a prism called this view of white light into question. Passing a beam of sunlight through a prism, he observed that the beam spread out into a colored band of light, called a spectrum. While others had undoubtedly performed similar experiments, Newton showed that the differences in color were caused by differing degrees of a property he called refrangibility. Refrangibility is the ability of light rays to be refracted, or bent by a substance. For example, when a ray of violet light passes through a refracting medium such as glass, it bends more than does a ray of red light. Newton concluded through experimentation that sunlight is a combination of all the colors of the spectrum and that the sunlight separates when passed through the prism because its component colors are of differing refrangibility. This property that Newton discovered actually depends directly on the wavelengths of the different components of sunlight. A refracting substance, such as a prism, will bend each wavelength of light by a different amount.

A The Reflecting Telescope

In October 1667, soon after his return to Cambridge, Newton was elected to a minor fellowship at Trinity College. Six months later he received a major fellowship and shortly thereafter was named Master of Arts. During this period he devoted much of his time to practical work in optics. His earlier experiments with the prism convinced him that a telescope’s resolution is limited not so much by the difficulty of building flawless lenses as by the general refraction differences of differently colored rays. Newton observed that lenses refract, or bend, different colors of light by a slightly different amount. He believed that these differences would make it impossible to bring a beam of white light (which includes all the different colors of light) to a single focus. Thus he turned his attention to building a reflecting telescope, or a telescope that uses mirrors instead of lenses, as a practical solution. Mirrors reflect all colors of light by the same amount.

Scottish mathematician James Gregory had proposed a design for a reflecting telescope in 1663, but Newton was the first scientist to build one. He built a reflecting telescope with a 1.3-in (3.3-cm) mirror in 1668. This telescope magnified objects about 40 times and differed slightly from Gregory’s in design. Three years later, the Royal Society, England’s official association of prominent scientists and mathematicians, invited Newton to submit his telescope for inspection. He sent one similar to his original model, and the Society established Newton’s dominance in the field by publishing a description of the instrument.

B Calculus (Newton’s “Fluxional Method”)

In 1669 Newton gave his Trinity mathematics professor Isaac Barrow an important manuscript, which is generally known by its shortened Latin title, De Analysi. This work contained many of Newton’s conclusions about calculus (what Newton called his “fluxional method”). Although the paper was not immediately published, Barrow made its results known to several of the leading mathematicians of Britain and Europe. This paper established Newton as one of the top mathematicians of his day and as the founder of modern calculus (along with Leibniz). Calculus addresses such concepts as the rate of change of a certain quantity, the slope of a curve at a given point, the computation of maximum and minimum values of functions, and the calculation of areas bounded by curves. When Barrow retired in 1669, he suggested to the college that Newton succeed him. Newton became the new professor of mathematics and chose optics as the subject of his first course of lectures.

C Newton’s First Published Works

In early 1672 Newton was elected a Fellow of the Royal Society. Shortly afterward Newton offered to submit a paper detailing his discovery of the composite nature of white light. Much impressed by his account, the Society published it. This publication triggered a long series of objections to Newton’s scientific views in general, mostly by European scientists from outside England. Many of the criticisms later proved unsound. The strongest criticism of Newton’s work, however, concerned his work on the theory of gravity and came from English inventor, mathematician, and curator of the Royal Society Robert Hooke. Hooke insisted that he had suggested fundamental principles of the law of gravitation to Newton. Newton answered these objections carefully and at first patiently but later with growing irritation. These public arguments aggravated Newton’s sensitivity to criticism, and for several years he stopped publishing his findings.

IV THE PRINCIPIA MATHEMATICA AND LAWS OF MOTION

By 1679 Newton had returned to the problem of planetary orbits. The idea of a planetary attraction based on the inverse square of the distance between the Sun and the planets (which he had assumed in his early calculations at Woolsthorpe) ignited wide debate in the scientific community. This law of attraction follows, in the simple case of a circular orbit, from German astronomer Johannes Kepler’s Third Law, which relates the time of a planet’s revolution around the Sun to the size of the planet’s orbit (see Kepler’s Laws). The law of attraction also takes into account the centripetal acceleration of a body moving in a circle, given by Dutch astronomer Christiaan Huygens in 1673. The problem of determining the orbit from the law of force had baffled everyone before Newton, who solved it in about 1680. See also Mechanics: Newton’s Three Laws of Motion.

In August 1684 English astronomer Edmond Halley visited Cambridge to consult with Newton on the problem of orbits. During a discussion with Halley about the shape of an orbit under the inverse square law of attraction, Newton suggested that it would be an ellipse. Unable to find the calculation from which he had derived the answer, Newton promised to send it to Halley, which he did a few months later. On a second visit Halley received what he called “a curious treatise de motu” (de motu means “on motion”), which at Halley’s request was registered with the Royal Society in February 1685.

This tract on the laws of motion formed the basis of the first book of Philosophiae Naturalis Principia Mathematica. Scientists and scholars consider this work a milestone of scientific inquiry, and its composition in the span of about 18 months was an intellectual feat unsurpassed at that time. Halley played a substantial role in the development of the Principia. He tactfully smoothed over differences between Newton and Hooke, who insisted that Newton had stolen some of his ideas. Newton angrily decided to suppress the third section of this work, but Halley persuaded Newton to publish it. Halley managed Newton’s work through publication and underwrote the cost of printing.

The Principia finally appeared in the summer of 1687. The scientific community hailed it as a masterpiece, although Newton had intentionally made the book difficult “to avoid being baited by little smatterers in mathematics.” The book’s grand unifying idea of gravitation, with effects extending throughout the solar system, captured the imagination of the scientific community. The work used one principle to explain diverse phenomena such as the tides, the irregularities of the Moon’s motion, and the slight yearly variations in the onset of spring and autumn.

V NEWTON’S LATER WORK

A few months before publication of the Principia, Newton emerged as a defender of academic freedom. King James II, who hoped to reestablish Roman Catholicism in England, issued a mandate to Cambridge in February 1687. This mandate called on the university to admit a certain Benedictine monk, Alban Francis, to the degree of Master of Arts without requiring him to take the usual oaths of allegiance to the Crown. The university saw this mandate as a request to grant preferential treatment to a Catholic and as a threat both to tradition and standards, so it steadfastly refused. Newton took a prominent part in defending the university’s position. The university senate appointed a group (including Newton) to appear before a government commission at Westminster, and they successfully defended the university’s rights. After the downfall of James II in the Glorious Revolution of 1688, Newton was elected a representative of the university in the Convention Parliament, in which he sat from January 1689 until its dissolution a year later. While he does not appear to have taken part in debate, Newton continued to be zealous in upholding the privileges of the university.

Newton’s public duties brought a change to his retiring mode of life and required frequent journeys to London, where he met several prominent writers and intellectuals, most notably philosopher John Locke and diarist and civil servant Samuel Pepys. In the early 1690s, possibly in response to the intellectual exertion of writing the Principia, Newton suffered a period of depression. Opinions differ among Newton’s biographers as to the permanence of the effects of the attack.

In the years after his illness, Newton summoned the energy to attack the complex problem of the Moon’s motion. This work involved a correspondence with John Flamsteed, England’s first Astronomer Royal, whose lunar observations Newton needed. However, misunderstandings and quarrels marred their relationship, which ended sourly. In 1698 Newton tried to carry his lunar work further and resumed collaboration with Flamsteed, but difficulties arose again and Newton accused Flamsteed of withholding his observations. The two scientists had not resolved the dispute when Flamsteed died in 1719.

In 1696 Newton’s friends in the government secured a paying political post for him by appointing him warden of the mint. This position required that he live in London, where he resided until his death. Newton’s work at the mint included a complete reform of the coinage. In order to combat counterfeiting, he introduced the minting of coins of standard weight and composition. He also instituted the policy of minting coins with milled edges. Newton successfully carried out these tasks, which demanded great technical and administrative skill, in the three years leading up to November 1699. At that time his peers promoted him to the mastership of the mint. This position was a well-paid post that Newton held for the rest of his life.

In 1701 Newton resigned his chair and fellowship at Cambridge and in 1703 was elected president of the Royal Society, an office to which he was reelected annually thereafter. In 1704, a year after the death of his rival Hooke, he brought out his second great treatise, Opticks, which included his theories of light and color as well as his mathematical discoveries. Unlike the Principia, which was in Latin, Opticks was written in English, but Newton later published a Latin translation. Most of Newton’s work on Opticks was done long before he relocated to London. One of its most interesting features is a series of general speculations added to the second edition (1717) in the form of “Queries,” or questions, which bear witness to his profound insight into physics. Many of his questions foreshadowed modern developments in physics, engineering, and the natural sciences.

In 1705 Queen Anne knighted Newton. By this time Newton was the dominant figure in British and European science. In the last two decades of his life, he prepared the second and third editions of the Principia (1713, 1726) and published second and third editions of Opticks (1717, 1721) as well.

During these last two decades Newton was entangled in a lengthy and bitter controversy with Leibniz over which of the two scientists had invented calculus. This controversy embittered Newton’s last years and harmed relations between the scientific communities in Britain and on the European continent. It also slowed the progress of mathematical science in Britain. Most scholars agree that Newton was the first to invent calculus, although Leibniz was the first to publish his findings. Mathematicians later adopted Leibniz’s mathematical symbols, which have survived to the present day with few changes.

VI NEWTON’S IMPACT ON SCIENCE

Newton’s place in scientific history rests on his application of mathematics to the study of nature and his explanation of a wide range of natural phenomena with one general principle—the law of gravitation. He used the foundations of dynamics, or the laws of nature governing motion and its effects on bodies, as the basis of a mechanical picture of the universe. His achievements in the use of calculus went so far beyond previous discoveries that scientists and scholars regard him as the chief pioneer in this field of mathematics.

Newton’s work greatly influenced the development of physical sciences. During the two centuries following publication of the Principia, scientists and philosophers found many new areas in which they applied Newton’s methods of inquiry and analysis. Much of this expansion arose as a consequence of the Principia. Scientists did not see the need for revision of some of Newton’s conclusions until the early 20th century. This reassessment of Newton’s ideas about the universe led to the modern theory of relativity and to quantum theory, which deal with the special cases of physics involving high speeds and physics of very small dimensions, respectively. For systems of ordinary dimensions, involving velocities that do not approach the speed of light, the principles that Newton formulated nearly three centuries ago are still valid.

Besides his scientific work, Newton left substantial writings on theology, chronology, alchemy, and chemistry. In 1725 Newton moved from London to Kensington (then a village outside London) for health reasons. He died there on March 20, 1727. He was buried in Westminster Abbey, the first scientist to be so honored.

Contributed By: Richard S. Westfall

Newton, Sir Isaac

b. Dec. 25, 1642 [Jan. 4, 1643, New Style], Woolsthorpe, Lincolnshire, Eng.

d. March 20 [March 31], 1727, London

English physicist and mathematician, who was the culminating figure of the scientific revolution of the 17th century. In optics, his discovery of the composition of white light integrated the phenomena of colours into the science of light and laid the foundation for modern physical optics. In mechanics, his three laws of motion, the basic principles of modern physics, resulted in the formulation of the law of universal gravitation. In mathematics, he was the original discoverer of the infinitesimal calculus. Newton's Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), 1687, was one of the most important single works in the history of modern science.

Formative influences

Born in the hamlet of Woolsthorpe, Newton was the only son of a local yeoman, also Isaac Newton, who had died three months before, and of Hannah Ayscough. That same year, at Arcetri near Florence, Galileo Galilei had died; Newton would eventually pick up his idea of a mathematical science of motion and bring his work to full fruition. A tiny and weak baby, Newton was not expected to survive his first day of life, much less 84 years. Deprived of a father before birth, he soon lost his mother as well, for within two years she married a second time; her husband, the well-to-do minister Barnabas Smith, left young Isaac with his grandmother and moved to a neighbouring village to raise a son and two daughters. For nine years, until the death of Barnabas Smith in 1653, Isaac was effectively separated from his mother, and his pronounced psychotic tendencies have been ascribed to this traumatic event. That he hated his stepfather we may be sure. When he examined the state of his soul in 1662 and compiled a catalog of sins in shorthand, he remembered "Threatning my father and mother Smith to burne them and the house over them." The acute sense of insecurity that rendered him obsessively anxious when his work was published and irrationally violent when he defended it accompanied Newton throughout his life and can plausibly be traced to his early years.

After his mother was widowed a second time, she determined that her first-born son should manage her now considerable property. It quickly became apparent, however, that this would be a disaster, both for the estate and for Newton. He could not bring himself to concentrate on rural affairs--set to watch the cattle, he would curl up under a tree with a book. Fortunately, the mistake was recognized, and Newton was sent back to the grammar school in Grantham, where he had already studied, to prepare for the university. As with many of the leading scientists of the age, he left behind in Grantham anecdotes about his mechanical ability and his skill in building models of machines, such as clocks and windmills. At the school he apparently gained a firm command of Latin but probably received no more than a smattering of arithmetic. By June 1661, he was ready to matriculate at Trinity College, Cambridge, somewhat older than the other undergraduates because of his interrupted education.

Influence of the scientific revolution

When Newton arrived in Cambridge in 1661, the movement now known as the scientific revolution was well advanced, and many of the works basic to modern science had appeared. Astronomers from Copernicus to Kepler had elaborated the heliocentric system of the universe. Galileo had proposed the foundations of a new mechanics built on the principle of inertia. Led by Descartes, philosophers had begun to formulate a new conception of nature as an intricate, impersonal, and inert machine. Yet as far as the universities of Europe, including Cambridge, were concerned, all this might well have never happened. They continued to be the strongholds of outmoded Aristotelianism, which rested on a geocentric view of the universe and dealt with nature in qualitative rather than quantitative terms.

Like thousands of other undergraduates, Newton began his higher education by immersing himself in Aristotle's work. Even though the new philosophy was not in the curriculum, it was in the air. Some time during his undergraduate career, Newton discovered the works of the French natural philosopher René Descartes and the other mechanical philosophers, who, in contrast to Aristotle, viewed physical reality as composed entirely of particles of matter in motion and who held that all the phenomena of nature result from their mechanical interaction. A new set of notes, which he entitled "Quaestiones Quaedam Philosophicae" ("Certain Philosophical Questions"), begun sometime in 1664, usurped the unused pages of a notebook intended for traditional scholastic exercises; under the title he entered the slogan "Amicus Plato amicus Aristoteles magis amica veritas" ("Plato is my friend, Aristotle is my friend, but my best friend is truth"). Newton's scientific career had begun.

The "Quaestiones" reveal that Newton had discovered the new conception of nature that provided the framework of the scientific revolution. He had thoroughly mastered the works of Descartes and had also discovered that the French philosopher Pierre Gassendi had revived atomism, an alternative mechanical system to explain nature. The "Quaestiones" also reveal that Newton already was inclined to find the latter a more attractive philosophy than Cartesian natural philosophy, which rejected the existence of ultimate indivisible particles. The works of the 17th-century chemist Robert Boyle provided the foundation for Newton's considerable work in chemistry. Significantly, he had read Henry More, the Cambridge Platonist, and was thereby introduced to another intellectual world, the magical Hermetic tradition, which sought to explain natural phenomena in terms of alchemical and magical concepts. The two traditions of natural philosophy, the mechanical and the Hermetic, antithetical though they appear, continued to influence his thought and in their tension supplied the fundamental theme of his scientific career.

Although he did not record it in the "Quaestiones," Newton had also begun his mathematical studies. He again started with Descartes, from whose La Géometrie he branched out into the other literature of modern analysis with its application of algebraic techniques to problems of geometry. He then reached back for the support of classical geometry. Within little more than a year, he had mastered the literature; and, pursuing his own line of analysis, he began to move into new territory. He discovered the binomial theorem, and he developed the calculus, a more powerful form of analysis that employs infinitesimal considerations in finding the slopes of curves and areas under curves.

By 1669 Newton was ready to write a tract summarizing his progress, De Analysi per Aequationes Numeri Terminorum Infinitas ("On Analysis by Infinite Series"), which circulated in manuscript through a limited circle and made his name known. During the next two years he revised it as De methodis serierum et fluxionum ("On the Methods of Series and Fluxions"). The word fluxions, Newton's private rubric, indicates that the calculus had been born. Despite the fact that only a handful of savants were even aware of Newton's existence, he had arrived at the point where he had become the leading mathematician in Europe.

Work during the plague years

When Newton received the bachelor's degree in April 1665, the most remarkable undergraduate career in the history of university education had passed unrecognized. On his own, without formal guidance, he had sought out the new philosophy and the new mathematics and made them his own, but he had confined the progress of his studies to his notebooks. Then, in 1665, the plague closed the university, and for most of the following two years he was forced to stay at his home, contemplating at leisure what he had learned. During the plague years Newton laid the foundations of the calculus and extended an earlier insight into an essay, "Of Colours," which contains most of the ideas elaborated in his Opticks. It was during this time that he examined the elements of circular motion and, applying his analysis to the Moon and the planets, derived the inverse square relation that the radially directed force acting on a planet decreases with the square of its distance from the Sun--which was later crucial to the law of universal gravitation. The world heard nothing of these discoveries.

Career

The optics

Inaugural lectures at Trinity

Newton was elected to a fellowship in Trinity College in 1667, after the university reopened. Two years later, Isaac Barrow, Lucasian professor of mathematics, who had transmitted Newton's De Analysi to John Collins in London, resigned the chair to devote himself to divinity and recommended Newton to succeed him. The professorship exempted Newton from the necessity of tutoring but imposed the duty of delivering an annual course of lectures. He chose the work he had done in optics as the initial topic; during the following three years (1670-72), his lectures developed the essay "Of Colours" into a form which was later revised to become Book One of his Opticks.

Beginning with Kepler's Paralipomena in 1604, the study of optics had been a central activity of the scientific revolution. Descartes's statement of the sine law of refraction, relating the angles of incidence and emergence at interfaces of the media through which light passes, had added a new mathematical regularity to the science of light, supporting the conviction that the universe is constructed according to mathematical regularities. Descartes had also made light central to the mechanical philosophy of nature; the reality of light, he argued, consists of motion transmitted through a material medium. Newton fully accepted the mechanical nature of light, although he chose the atomistic alternative and held that light consists of material corpuscles in motion. The corpuscular conception of light was always a speculative theory on the periphery of his optics, however. The core of Newton's contribution had to do with colours. An ancient theory extending back at least to Aristotle held that a certain class of colour phenomena, such as the rainbow, arises from the modification of light, which appears white in its pristine form. Descartes had generalized this theory for all colours and translated it into mechanical imagery. Through a series of experiments performed in 1665 and 1666, in which the spectrum of a narrow beam was projected onto the wall of a darkened chamber, Newton denied the concept of modification and replaced it with that of analysis. Basically, he denied that light is simple and homogeneous--stating instead that it is complex and heterogeneous and that the phenomena of colours arise from the analysis of the heterogeneous mixture into its simple components. The ultimate source of Newton's conviction that light is corpuscular was his recognition that individual rays of light have immutable properties; in his view, such properties imply immutable particles of matter. He held that individual rays (that is, particles of given size) excite sensations of individual colours when they strike the retina of the eye. He also concluded that rays refract at distinct angles--hence, the prismatic spectrum, a beam of heterogeneous rays, i.e., alike incident on one face of a prism, separated or analyzed by the refraction into its component parts--and that phenomena such as the rainbow are produced by refractive analysis. Because he believed that chromatic aberration could never be eliminated from lenses, Newton turned to reflecting telescopes; he constructed the first ever built. The heterogeneity of light has been the foundation of physical optics since his time.

There is no evidence that the theory of colours, fully described by Newton in his inaugural lectures at Cambridge, made any impression, just as there is no evidence that aspects of his mathematics and the content of the Principia, also pronounced from the podium, made any impression. Rather, the theory of colours, like his later work, was transmitted to the world through the Royal Society of London, which had been organized in 1660. When Newton was appointed Lucasian professor, his name was probably unknown in the Royal Society; in 1671, however, they heard of his reflecting telescope and asked to see it. Pleased by their enthusiastic reception of the telescope and by his election to the society, Newton volunteered a paper on light and colours early in 1672. On the whole, the paper was also well received, although a few questions and some dissent were heard.

Controversy

Among the most important dissenters to Newton's paper was Robert Hooke, one of the leaders of the Royal Society who considered himself the master in optics and hence he wrote a condescending critique of the unknown parvenu. One can understand how the critique would have annoyed a normal man. The flaming rage it provoked, with the desire publicly to humiliate Hooke, however, bespoke the abnormal. Newton was unable rationally to confront criticism. Less than a year after submitting the paper, he was so unsettled by the give and take of honest discussion that he began to cut his ties, and he withdrew into virtual isolation.

In 1675, during a visit to London, Newton thought he heard Hooke accept his theory of colours. He was emboldened to bring forth a second paper, an examination of the colour phenomena in thin films, which was identical to most of Book Two as it later appeared in the Opticks. The purpose of the paper was to explain the colours of solid bodies by showing how light can be analyzed into its components by reflection as well as refraction. His explanation of the colours of bodies has not survived, but the paper was significant in demonstrating for the first time the existence of periodic optical phenomena. He discovered the concentric coloured rings in the thin film of air between a lens and a flat sheet of glass; the distance between these concentric rings (Newton's rings) depends on the increasing thickness of the film of air. In 1704 Newton combined a revision of his optical lectures with the paper of 1675 and a small amount of additional material in his Opticks.

A second piece which Newton had sent with the paper of 1675 provoked new controversy. Entitled "An Hypothesis Explaining the Properties of Light," it was in fact a general system of nature. Hooke apparently claimed that Newton had stolen its content from him, and Newton boiled over again. The issue was quickly controlled, however, by an exchange of formal, excessively polite letters that fail to conceal the complete lack of warmth between the men.

Newton was also engaged in another exchange on his theory of colours with a circle of English Jesuits in Liège, perhaps the most revealing exchange of all. Although their objections were shallow, their contention that his experiments were mistaken lashed him into a fury. The correspondence dragged on until 1678, when a final shriek of rage from Newton, apparently accompanied by a complete nervous breakdown, was followed by silence. The death of his mother the following year completed his isolation. For six years he withdrew from intellectual commerce except when others initiated a correspondence, which he always broke off as quickly as possible.

Influence of the Hermetic tradition

During his time of isolation, Newton was greatly influenced by the Hermetic tradition with which he had been familiar since his undergraduate days. Newton, always somewhat interested in alchemy, now immersed himself in it, copying by hand treatise after treatise and collating them to interpret their arcane imagery. Under the influence of the Hermetic tradition, his conception of nature underwent a decisive change. Until that time, Newton had been a mechanical philosopher in the standard 17th-century style, explaining natural phenomena by the motions of particles of matter. Thus, he held that the physical reality of light is a stream of tiny corpuscles diverted from its course by the presence of denser or rarer media. He felt that the apparent attraction of tiny bits of paper to a piece of glass that has been rubbed with cloth results from an ethereal effluvium that streams out of the glass and carries the bits of paper back with it. This mechanical philosophy denied the possibility of action at a distance; as with static electricity, it explained apparent attractions away by means of invisible ethereal mechanisms. Newton's "Hypothesis of Light" of 1675, with its universal ether, was a standard mechanical system of nature. Some phenomena, such as the capacity of chemicals to react only with certain others, puzzled him, however, and he spoke of a "secret principle" by which substances are "sociable" or "unsociable" with others. About 1679, Newton abandoned the ether and its invisible mechanisms and began to ascribe the puzzling phenomena--chemical affinities, the generation of heat in chemical reactions, surface tension in fluids, capillary action, the cohesion of bodies, and the like--to attractions and repulsions between particles of matter. More than 35 years later, in the second English edition of the Opticks, Newton accepted an ether again, although it was an ether that embodied the concept of action at a distance by positing a repulsion between its particles. The attractions and repulsions of Newton's speculations were direct transpositions of the occult sympathies and antipathies of Hermetic philosophy--as mechanical philosophers never ceased to protest. Newton, however, regarded them as a modification of the mechanical philosophy that rendered it subject to exact mathematical treatment. As he conceived of them, attractions were quantitatively defined, and they offered a bridge to unite the two basic themes of 17th-century science--the mechanical tradition, which had dealt primarily with verbal mechanical imagery, and the Pythagorean tradition, which insisted on the mathematical nature of reality. Newton's reconciliation through the concept of force was his ultimate contribution to science.

The Principia

Planetary motion

The title page from Newton's De Philosophiae Naturalis Principia Mathematica, London, 1687.

Newton originally applied the idea of attractions and repulsions solely to the range of terrestrial phenomena mentioned in the preceding paragraph. But late in 1679, not long after he had embraced the concept, another application was suggested in a letter from Hooke, who was seeking to renew correspondence. Hooke mentioned his analysis of planetary motion--in effect, the continuous diversion of a rectilinear motion by a central attraction. Newton bluntly refused to correspond but, nevertheless, went on to mention an experiment to demonstrate the rotation of the Earth: let a body be dropped from a tower; because the tangential velocity at the top of the tower is greater than that at the foot, the body should fall slightly to the east. He sketched the path of fall as part of a spiral ending at the centre of the Earth. This was a mistake, as Hooke pointed out; according to Hooke's theory of planetary motion, the path should be elliptical, so that if the Earth were split and separated to allow the body to fall, it would rise again to its original location. Newton did not like being corrected, least of all by Hooke, but he had to accept the basic point; he corrected Hooke's figure, however, using the assumption that gravity is constant. Hooke then countered by replying that, although Newton's figure was correct for constant gravity, his own assumption was that gravity decreases as the square of the distance. Several years later, this letter became the basis for Hooke's charge of plagiarism. He was mistaken in the charge. His knowledge of the inverse square relation rested only on intuitive grounds; he did not derive it properly from the quantitative statement of centripetal force and Kepler's third law, which relates the periods of planets to the radii of their orbits. Moreover, unknown to him, Newton had so derived the relation more than ten years earlier. Nevertheless, Newton later confessed that the correspondence with Hooke led him to demonstrate that an elliptical orbit entails an inverse square attraction to one focus--one of the two crucial propositions on which the law of universal gravitation would ultimately rest. What is more, Hooke's definition of orbital motion--in which the constant action of an attracting body continuously pulls a planet away from its inertial path--suggested a cosmic application for Newton's concept of force and an explanation of planetary paths employing it. In 1679 and 1680, Newton dealt only with orbital dynamics; he had not yet arrived at the concept of universal gravitation.

Universal gravitation

Nearly five years later, in August 1684, Newton was visited by the British astronomer Edmond Halley, who was also troubled by the problem of orbital dynamics. Upon learning that Newton had solved the problem, he extracted Newton's promise to send the demonstration. Three months later he received a short tract entitled De Motu ("On Motion"). Already Newton was at work improving and expanding it. In two and a half years, the tract De Motu grew into Philosophiae Naturalis Principia Mathematica, which is not only Newton's masterpiece but also the fundamental work for the whole of modern science.

Significantly, De Motu did not state the law of universal gravitation. For that matter, even though it was a treatise on planetary dynamics, it did not contain any of the three Newtonian laws of motion. Only when revising De Motu did Newton embrace the principle of inertia (the first law) and arrive at the second law of motion. The second law, the force law, proved to be a precise quantitative statement of the action of the forces between bodies that had become the central members of his system of nature. By quantifying the concept of force, the second law completed the exact quantitative mechanics that has been the paradigm of natural science ever since.

The quantitative mechanics of the Principia is not to be confused with the mechanical philosophy. The latter was a philosophy of nature that attempted to explain natural phenomena by means of imagined mechanisms among invisible particles of matter. The mechanics of the Principia was an exact quantitative description of the motions of visible bodies. It rested on Newton's three laws of motion: (1) that a body remains in its state of rest unless it is compelled to change that state by a force impressed on it; (2) that the change of motion (the change of velocity times the mass of the body) is proportional to the force impressed; (3) that to every action there is an equal and opposite reaction. The analysis of circular motion in terms of these laws yielded a formula of the quantitative measure, in terms of a body's velocity and mass, of the centripetal force necessary to divert a body from its rectilinear path into a given circle. When Newton substituted this formula into Kepler's third law, he found that the centripetal force holding the planets in their given orbits about the Sun must decrease with the square of the planets' distances from the Sun. Because the satellites of Jupiter also obey Kepler's third law, an inverse square centripetal force must also attract them to the centre of their orbits. Newton was able to show that a similar relation holds between the Earth and its Moon. The distance of the Moon is approximately 60 times the radius of the Earth. Newton compared the distance by which the Moon, in its orbit of known size, is diverted from a tangential path in one second with the distance that a body at the surface of the Earth falls from rest in one second. When the latter distance proved to be 3,600 (60 60) times as great as the former, he concluded that one and the same force, governed by a single quantitative law, is operative in all three cases, and from the correlation of the Moon's orbit with the measured acceleration of gravity on the surface of the Earth, he applied the ancient Latin word gravitas (literally, "heaviness" or "weight") to it. The law of universal gravitation, which he also confirmed from such further phenomena as the tides and the orbits of comets, states that every particle of matter in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

When the Royal Society received the completed manuscript of Book I in 1686, Hooke raised the cry of plagiarism, a charge that cannot be sustained in any meaningful sense. On the other hand, Newton's response to it reveals much about him. Hooke would have been satisfied with a generous acknowledgment; it would have been a graceful gesture to a sick man already well into his decline, and it would have cost Newton nothing. Newton, instead, went through his manuscript and eliminated nearly every reference to Hooke. Such was his fury that he refused either to publish his Opticks or to accept the presidency of the Royal Society until Hooke was dead.

International prominence

The Principia immediately raised Newton to international prominence. In their continuing loyalty to the mechanical ideal, Continental scientists rejected the idea of action at a distance for a generation, but even in their rejection they could not withhold their admiration for the technical expertise revealed by the work. Young British scientists spontaneously recognized him as their model. Within a generation the limited number of salaried positions for scientists in England, such as the chairs at Oxford, Cambridge, and Gresham College, were monopolized by the young Newtonians of the next generation. Newton, whose only close contacts with women were his unfulfilled relationship with his mother, who had seemed to abandon him, and his later guardianship of a niece, found satisfaction in the role of patron to the circle of young scientists. His friendship with Fatio de Duillier, a Swiss-born mathematician resident in London who shared Newton's interests, was the most profound experience of his adult life.

Warden of the mint

Almost immediately following the Principia's publication, Newton, a fervent if unorthodox Protestant, helped to lead the resistance of Cambridge to James II's attempt to Catholicize it. As a consequence, he was elected to represent the university in the convention that arranged the revolutionary settlement. In this capacity, he made the acquaintance of a broader group, including the philosopher John Locke. Newton tasted the excitement of London life in the aftermath of the Principia. The great bulk of his creative work had been completed. He was never again satisfied with the academic cloister, and his desire to change was whetted by Fatio's suggestion that he find a position in London. Seek a place he did, especially through the agency of his friend, the rising politician Charles Montague, later Lord Halifax. Finally, in 1696, he was appointed warden of the mint. Although he did not resign his Cambridge appointments until 1701, he moved to London and henceforth centred his life there.

In the meantime, Newton's relations with Fatio had undergone a crisis. Fatio was taken seriously ill; then family and financial problems threatened to call him home to Switzerland. Newton's distress knew no limits. In 1693 he suggested that Fatio move to Cambridge, where Newton would support him, but nothing came of the proposal. Through early 1693 the intensity of Newton's letters built almost palpably, and then, without surviving explanation, both the close relationship and the correspondence broke off. Four months later, without prior notice, Samuel Pepys and John Locke, both personal friends of Newton, received wild, accusatory letters. Pepys was informed that Newton would see him no more; Locke was charged with trying to entangle him with women. Both men were alarmed for Newton's sanity; and, in fact, Newton had suffered at least his second nervous breakdown. The crisis passed, and Newton recovered his stability. Only briefly did he ever return to sustained scientific work, however, and the move to London was the effective conclusion of his creative activity.

As warden and then master of the mint, Newton drew a large income, as much as 2,000 per annum. Added to his personal estate, the income left him a rich man at his death. The position, regarded as a sinecure, was treated otherwise by Newton. During the great recoinage, there was need for him to be actively in command; even afterward, however, he chose to exercise himself in the office. Above all, he was interested in counterfeiting. He became the terror of London counterfeiters, sending a goodly number to the gallows and finding in them a socially acceptable target on which to vent the rage that continued to well up within him.

Interest in religion and theology

Newton found time now to explore other interests, such as religion and theology. In the early 1690s he had sent Locke a copy of a manuscript attempting to prove that Trinitarian passages in the Bible were latter-day corruptions of the original text. When Locke made moves to publish it, Newton withdrew in fear that his anti-Trinitarian views would become known. In his later years, he devoted much time to the interpretation of the prophecies of Daniel and St. John, and to a closely related study of ancient chronology. Both works were published after his death.

Leader of English science

In London, Newton assumed the role of patriarch of English science. In 1703 he was elected President of the Royal Society. Four years earlier, the French Académie des Sciences (Academy of Sciences) had named him one of eight foreign associates. In 1705 Queen Anne knighted him, the first occasion on which a scientist was so honoured. Newton ruled the Royal Society magisterially. John Flamsteed, the Astronomer Royal, had occasion to feel that he ruled it tyrannically. In his years at the Royal Observatory at Greenwich, Flamsteed, who was a difficult man in his own right, had collected an unrivalled body of data. Newton had received needed information from him for the Principia, and in the 1690s, as he worked on the lunar theory, he again required Flamsteed's data. Annoyed when he could not get all the information he wanted as quickly as he wanted it, Newton assumed a domineering and condescending attitude toward Flamsteed. As president of the Royal Society, he used his influence with the government to be named as chairman of a body of "visitors" responsible for the Royal Observatory; then he tried to force the immediate publication of Flamsteed's catalog of stars. The disgraceful episode continued for nearly 10 years. Newton would brook no objections. He broke agreements that he had made with Flamsteed. Flamsteed's observations, the fruit of a lifetime of work, were, in effect, seized despite his protests and prepared for the press by his mortal enemy, Edmond Halley. Flamsteed finally won his point and by court order had the printed catalog returned to him before it was generally distributed. He burned the printed sheets, and his assistants brought out an authorized version after his death. In this respect, and at considerable cost to himself, Flamsteed was one of the few men to best Newton. Newton sought his revenge by systematically eliminating references to Flamsteed's help in later editions of the Principia.

In Gottfried Wilhelm Leibniz, the German philosopher and mathematician, Newton met a contestant more of his own calibre. It is now well established that Newton developed the calculus before Leibniz seriously pursued mathematics. It is almost universally agreed that Leibniz later arrived at the calculus independently. There has never been any question that Newton did not publish his method of fluxions; thus, it was Leibniz's paper in 1684 that first made the calculus a matter of public knowledge. In the Principia Newton hinted at his method, but he did not really publish it until he appended two papers to the Opticks in 1704. By then the priority controversy was already smouldering. If, indeed, it mattered, it would be impossible finally to assess responsibility for the ensuing fracas. What began as mild innuendoes rapidly escalated into blunt charges of plagiarism on both sides. Egged on by followers anxious to win a reputation under his auspices, Newton allowed himself to be drawn into the centre of the fray; and, once his temper was aroused by accusations of dishonesty, his anger was beyond constraint. Leibniz's conduct of the controversy was not pleasant, and yet it paled beside that of Newton. Although he never appeared in public, Newton wrote most of the pieces that appeared in his defense, publishing them under the names of his young men, who never demurred. As president of the Royal Society, he appointed an "impartial" committee to investigate the issue, secretly wrote the report officially published by the society, and reviewed it anonymously in the Philosophical Transactions. Even Leibniz's death could not allay Newton's wrath, and he continued to pursue the enemy beyond the grave. The battle with Leibniz, the irrepressible need to efface the charge of dishonesty, dominated the final 25 years of Newton's life. It obtruded itself continually upon his consciousness. Almost any paper on any subject from those years is apt to be interrupted by a furious paragraph against the German philosopher, as he honed the instruments of his fury ever more keenly. In the end, only Newton's death ended his wrath.

Final years

During his final years Newton brought out further editions of his central works. After the first edition of the Opticks in 1704, which merely published work done 30 years before, he published a Latin edition in 1706 and a second English edition in 1717-18. In both, the central text was scarcely touched, but he did expand the "Queries" at the end into the final statement of his speculations on the nature of the universe. The second edition of the Principia, edited by Roger Cotes in 1713, introduced extensive alterations. A third edition, edited by Henry Pemberton in 1726, added little more. Until nearly the end, Newton presided at the Royal Society (frequently dozing through the meetings) and supervised the mint. During his last years, his niece, Catherine Barton Conduitt, and her husband lived with him.

Major Works

Philosophiae Naturalis Principia Mathematica (1687; Mathematical Principles of Natural Philosophy, 1729); Opticks (1704); Arithmetica Universalis (1707; Universal Arithmetick, 1720); The Chronology of Ancient Kingdoms Amended (1728); Observations Upon the Prophecies of Daniel and the Apocalypse of St. John (1733).

Bibliography

I. Bernard Cohen, Introduction to Newton's "Principia" (1971), a history of the development and modification of Newton's major work, is the first volume of Cohen's edition of the Principia and includes variant readings. Additional collections of Newtonian materials, all with valuable introductory essays, include D.T. Whiteside (ed.), The Mathematical Papers of Isaac Newton, 8 vol. (1967-81); A. Rupert Hall and Marie Boas Hall (eds. and trans.), Unpublished Scientific Papers of Isaac Newton (1962, reissued 1978); I. Bernard Cohen and Robert E. Schofield (eds.), Isaac Newton's Papers & Letters on Natural Philosophy and Related Documents, 2nd ed. (1978); and H.W. Turnbull et al. (eds.), Correspondence, 7 vol. (1959-77), a collection of Newton's letters, 1661-1727. Peter Wallis and Ruth Wallis, Newton and Newtoniana, 1672-1975 (1977), is a bibliography.

A standard biography of Newton is David Brewster, Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton, 2 vol. (1855, reprinted 1965). A more modern work by Richard S. Westfall, Never at Rest: A Biography of Isaac Newton (1980, reissued 1990), also available in a shorter version, The Life of Isaac Newton (1993), is a comprehensive study of Newton in light of new scholarship. Gale E. Christianson, In the Presence of the Creator: Isaac Newton and His Times (1984), includes much contextual information. Frank E. Manuel, A Portrait of Isaac Newton (1968, reprinted 1990), offers a fascinating Freudian analysis, and his The Religion of Isaac Newton (1974) is a thorough discussion of his religious thought. Derek Gjertsen, The Newton Handbook (1986), comprises hundreds of brief entries on topics related to Newton and his era.

General treatments of the major problems in Newtonian science are found in Cohen's Franklin and Newton (1956, reissued 1966); John Fauvel (ed.), Let Newton Be! (1988), a collection of essays on Newton and his work, with illustrations; and A. Rupert Hall, Isaac Newton, Adventurer in Thought (1992), a summary of recent research. John Herivel, The Background to Newton's Principia: A Study of Newton's Dynamical Researches in the Years 1664-84 (1965); and Richard S. Westfall, Force in Newton's Physics (1971), explore the development of Newton's mechanics. Newton's Optiks is treated in Hall's All Was Light (1993). Betty Jo Teeter Dobbs, The Foundations of Newton's Alchemy (1975, reissued 1983), and The Janus Faces of Genius (1991), examine Newton's alchemical studies. Cohen's The Newtonian Revolution (1980), evaluates the historical importance of Newton's style of scientific thought. Alexandre Koyré, Newtonian Studies (1965), contains a collection of essays by one of the master historians of science. Phillip Bricker and R.I.G. Hughes (eds.), Philosophical Perspectives on Newtonian Science (1990), is an advanced treatment, requiring familiarity with Newton's texts.