Isaac Newton

I

INTRODUCTION

Isaac Newton (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.