SOURCE: "System of the World," in Books That Changed the World, Second Edition, American Library Association, 1978, pp. 334-74.

[In the following essay, Downs surveys the content, scope, and reception of Newton's Principia.]

Sir Isaac Newton. Principia Mathematica

Of all the books which have profoundly influenced human affairs, few have been more celebrated and none read by fewer people than Sir Isaac Newton's Philosophiae Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"). Deliberately written in the most abstruse and technical Latin, profusely illustrated by complex geometrical diagrams, the work's direct audience has been limited to highly erudite astronomers, mathematicians, and physicists.

One of Newton's chief biographers has stated that when the Principia was published in the last quarter of the seventeenth century there were not more than three or four men living who could comprehend it; another generously stretched the number to ten or a dozen. The author himself admitted that it was "a hard book," but he had no apologies, for he planned it that way, making no concessions to the mathematically illiterate.

Yet, notable men of science hold Newton to be one of the great intellectual figures of all time. Laplace, a brilliant French astronomer, termed the Principia "preeminent above any other production of human genius." Lagrange, famous mathematician, asserted that Newton was the greatest genius who ever lived. Boltzmann, a pioneer of modern mathematical physics, called the Principia the first and greatest work ever written on theoretical physics. An eminent American astronomer, W. W. Campbell, remarked, "To me it is clear that Sir Isaac Newton, easily the greatest man of physical science in historic time, was uniquely the great pioneer of astro-physics." Comments from other leading scientists over the past two-and-a-half centuries have been phrased in like superlatives. The layman must necessarily accept these judgments on faith, and on the basis of results.

Newton was born almost exactly a century after the death of Copernicus, and in the same year as Galileo's death. These giants in the world of astronomy, together with Johannes Kepler, furnished the foundations upon which Newton continued to build.

Newton was a mathematical wizard in an age of gifted mathematicians. As Marvin pointed out, "the seventeenth century was the flowering age of mathematics, as the eighteenth was of chemistry and the nineteenth of biology, and the last four decades of the seventeenth saw more forward steps taken than any other period in history." Newton combined in himself the major physical sciences—mathematics, chemistry, physics, and astronomy—for in the seventeenth century, before the era of extreme specialization, a scientist could encompass all fields.

Newton, born on Christmas Day, 1642, in his early years saw the rise and fall of Oliver Cromwell's Commonwealth Government, the Great Fire which practically destroyed London, and the Great Plague which wiped out a third of the city's population. After eighteen years spent in the little hamlet of Woolsthorpe, Newton was sent to Cambridge University. There he was fortunate to come under the guidance of an able and inspiring teacher, Isaac Barrow, professor of mathematics, who has been called Newton's "intellectual father." Barrow recognized, encouraged, and stimulated the growing genius of young Newton. While still in college, Newton discovered the binomial theorem.

Because of the plague, Cambridge was closed in 1665, and Newton returned to the country. For the next two years, largely cut off from the world, he devoted himself to scientific experimentation and meditation. The consequences were astounding. Before he had reached the age of twenty-five, Newton had made three discoveries that entitle him to be ranked among the supreme scientific minds of all time. First was the invention of the differential calculus, termed "fluxions" by Newton, because it deals with variable or "flowing" quantities. The calculus is involved in all problems of flow, movement of bodies, and waves, and is essential to the solution of physical problems concerned with any kind of movement. "It seemed to unlock the gates guarding the storehouse of mathematical treasures; to lay the mathematical world at the feet of Newton and his followers," according to one commentator.

Newton's second major discovery was the law of composition of light, from which he proceeded to analyze the nature of color and of white light. It was shown that the white light of the sun is compounded of rays of light of all the colors of the rainbow. Color is therefore a characteristic of light, and the appearance of white light—as Newton's experiments with a prism demonstrated—comes from mixing the colors of the spectrum. Through knowledge gained from this discovery, Newton was able to construct the first satisfactory reflecting telescope.

Even more noteworthy was Newton's third revelation: the law of universal gravitation, which is said to have stirred the imaginations of scientists more than any theoretical discovery of modern times. According to a well-known anecdote, the flash of intuition which came to Newton when he observed the fall of an apple led to formulation of the law. There was nothing particularly new in the idea of the earth's attraction for bodies near its surface. Newton's great contribution was in conceiving the gravitation law to be universal in application—a force no less powerful in relation to celestial bodies than to the earth—and then producing mathematical proof of his theory.

Curiously enough, Newton published nothing at the time on these three highly significant discoveries on the calculus, color, and gravitation. Possessed of an extremely reticent, even secretive nature, he had an almost morbid dislike of public attention and controversy. Consequently, he was inclined to suppress the results of his experiments. Whatever he published later was done under pressure from friends, and afterward he nearly always regretted surrendering to their entreaties. Publication led to criticism and discussion of his work by fellow-scientists, something which Newton, with his sensitive nature, completely detested and resented.

Following the enforced isolation and leisure of the plague years, Newton returned to Cambridge, received a master's degree, and was appointed a fellow of Trinity College. Shortly thereafter his old teacher, Barrow, withdrew, and Newton, at the age of twenty-seven, became professor of mathematics, a position which he held for the next twenty-seven years. For the next decade or two little was heard of Newton. It is known that he continued his investigations of light, and published a paper on his discovery of the composite nature of white light. Immediately he became involved in controversy, first because his conclusions on the subject of light were in opposition to those then prevailing; and, second, because he had included in the paper a statement on his philosophy of science. In the latter, he had expressed the point of view that the chief function of science is to carry out carefully planned experiments, to record observations of the experiments, and lastly to prepare mathematical laws based on the results. As Newton stated it, the "proper method for enquiring after the properties of things is to deduce them from experiments." While these principles are in complete accord with modern scientific research, they were by no means filly accepted in Newton's day. Beliefs founded on imagination, reason, and the appearance of things, usually inherited from ancient philosophers, were preferred to experimental evidence.

Attacks on his paper by such established scientists as Huygens and Hooke so angered Newton that he resolved to escape future irritations by doing no more publishing. "I was so persecuted," he said, "with discussions arising from the publication of my theory of light, that I blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow." He even expressed an acute distaste for science itself, insisting that he had lost his former "affection" for it. Later, he had to be "spurred, cajoled and importuned" into writing his greatest work, the Principia. In fact, creation of the Principia appears to have come about more or less by chance.

In 1684, through computations by Picard, the earth's exact circumference was determined for the first time. Using the French astronomer's data, Newton applied the principle of gravitation to prove that the power which guides the moon around the earth and the planets around the sun is the force of gravity. The force varies directly with the mass of the attracted bodies and inversely as the square of their distances. Newton went on to show that this accounts for the elliptical orbits of the planets. The pull of gravity kept the moon and the planets in their paths, balancing the centrifugal forces of their motions.

Again, Newton failed to reveal his phenomenal discovery of nature's greatest secret. As it happened, however, other scientists were engaged in a search for a solution of the same problem. Several astronomers had suggested that the planets were bound to the sun by the force of gravity. Among these was Robert Hooke, Newton's severest and most persistent critic. But none of the theorists had been able to offer mathematical proof. By now Newton had won considerable reputation as a mathematician, and he was visited at Cambridge by the astronomer Edmund Halley who requested his help. When Halley stated the problem, he learned that it had been solved two years before by Newton. Further, Newton had worked out the principal laws of motion of bodies moving under the force of gravity. Characteristically, though, Newton had no intention of publishing his findings.

Halley at once recognized the significance of Newton's accomplishment, and used all his powers of persuasion to convince the stubborn Newton that his discovery should be developed and exploited. Moved by Halley's enthusiasm and with his own interest rekindled, Newton began the writing of his masterpiece, the Principia, termed by Langer "a veritable reservoir of mechanistic philosophy, one of the most original works ever produced."

Not the least remarkable feature of the Principia was that its composition was completed in eighteen months, during which, it is said, Newton was so engrossed that he often went without food and took little time to sleep. Only the most intense and prolonged concentration could have brought forth such a monumental intellectual achievement in so brief a period. It left Newton mentally and physically exhausted.

Furthermore, during the time of writing, Newton's peace of mind was intensely disturbed by the usual controversies, particularly with Hooke, who maintained he should receive credit for originating the theory that the motion of the planets could be explained by an inverse square law of attraction. Newton, who had finished two-thirds of the Principia, was so incensed by what he considered an unjustified claim, that he threatened to omit the third and most important section of his treatise. Again Halley used his influence and prevailed on Newton to complete the work as first planned.

The role played by Edmund Halley in the whole history of the Principia deserves the highest commendation. Not only was he responsible for inducing Newton to undertake the work in the first place, but he obtained an agreement with the Royal Society to publish it, and unselfishly dropped everything he was doing to supervise the final printing. Finally, when the Royal Society reneged on its promise to finance the publication, Halley stepped in and paid the entire expense out of his own pocket, though he was a man of moderate means, with a family to support.

Surmounting all obstacles, the Principia came from the press in 1687, in a small edition, selling for ten or twelve shillings a copy. The title page bore the imprimatur of Samuel Pepys, then President of the Royal Society, "although it is to be doubted," remarked one commentator, "whether the learned diarist could have understood so much as a single sentence of it."

Any brief summary of the Principia in nontechnical language is a difficult, if not impossible, undertaking, but some highlights may be indicated. The work as a whole deals with the motions of bodies treated mathematically, in particular, the application of dynamics and universal gravitation to the solar system. It begins with an explanation of the differential calculus or "fluxions," invented by Newton and used as a tool for calculations throughout the Principia. There follow definitions of the meaning of space and time, and a statement of the laws of motion, as formulated by Newton, with illustrations of their application. The fundamental principle is stated that every particle of matter is attracted by every other particle of matter with a force inversely proportional to the square of their distances apart. Also given are the laws governing the problem of bodies colliding with each other. Everything is expressed in classical geometrical forms.

The first book of the Principia is concerned with the motion of bodies in free space, while the second treats of "motion in a resisting medium," such as water. In the latter section, the complex problems of the motion of fluids are considered and solved, methods discussed for determining the velocity of sound, and wave motions described mathematically. Herein is laid the groundwork for the modern science of mathematical physics, hydrostatics, and hydrodynamics.

In the second book Newton effectively demolished the world system of Descartes, then in popular vogue. According to Descartes' theory, the motions of the heavenly bodies were due to vortexes. All space is filled with a thin fluid, and at certain points the fluid matter forms vortexes. For example, the solar system has fourteen vortexes, the largest of them containing the sun. The planets are carried around like chips in an eddy. These whirlpools were Descartes' explanation for the phenomena of gravitation. Newton proceeded to demonstrate experimentally and mathematically that "the Vortex Theory is in complete conflict with astronomical facts, and so far from explaining celestial motions would tend to upset them."

In the third book, entitled "The System of the World," Newton was at his greatest as he dealt with the astronomical consequences of the law of gravitation.

In the preceding books I have laid down the principles of philosophy [science]; principles not philosophical but mathematical.… These principles are the laws and conditions of certain motions, and powers or forces.… I have illustrated them here and there … with … an account of such things as are of more general nature … such as the density and the resistance of bodies, spaces void of all bodies, and the motion of light and sound. It remains that, from the same principles, I now demonstrate the frame of the System of the World.

Explaining why he had not popularized his work, Newton revealed that—

Upon this subject I had, indeed, composed the third Book in a popular method, that it might be read by many, but afterwards, considering that such as had not sufficiently entered into the principles could not easily discern the strength of the consequences, nor lay aside the prejudices to which they had been many years accustomed, therefore, to prevent the disputes which might be raised upon such accounts, I chose to reduce the substance of this Book in the form of Propositions (in the mathematical way), which should be read by those only who had first made themselves masters of the principles established in the preceding Books; not that I would advise anyone to the previous study of every Proposition of those Books; for they abound with such as might cost too much time, even to readers of good mathematical learning.

For this reason, the style of the Principia has been described as "glacial remoteness, written in the aloof manner of a high priest."

At the outset, Newton makes a fundamental break with the past by insisting that there is no difference between earthly and celestial phenomena. "Like effects in nature are produc'd by like causes," he asserted, "as breathing in man and in beast, the fall of stones in Europe and in America, the light of the kitchen fire and of the sun, the reflection of light on the earth and on the planets." Thus was discarded the ancient belief that other worlds are perfect and only the earth is imperfect. Now all were governed by the same rational laws, "bringing order and system," as John MacMurray said, "where chaos and mystery had reigned before."

A mere listing of the principal topics covered in the third book is impressive. The motions of the planets and of the satellites around the planets are established; methods for measuring the masses of the sun and planets are shown; and the density of the earth, the precession of the equinoxes, theory of tides, orbits of the comets, the moon's motion, and related matters discussed and resolved.

By his theory of "perturbations" Newton proved that the moon is attracted by both the earth and the sun, and therefore the moon's orbit is disturbed by the sun's pull, though the earth provides the stronger attraction. Likewise, the planets are subject to perturbations. The sun is not the stationary center of the universe, contrary to previous beliefs, but is attracted by the planets, just as they are attracted to it, and moves in the same way. In later centuries, application of the perturbations theory led to the discovery of the planets Neptune and Pluto.

The masses of different planets and the masses of the sun Newton determined by relating them to the earth's mass. He estimated that the earth's density is between five and six times that of water (the figure used by scientists today is 5.5), and on this basis Newton calculated the masses of the sun and of the planets with satellites, an achievement which Adam Smith called "above the reach of human reason and experience."

Next, the fact that the earth is not an exact sphere, but is flattened at the poles because of rotation, was explained, and the amount of flattening was calculated. Because of the flattening at the poles and the slight bulge at the equator, Newton deducted that the force of gravity must be less at the poles than at the equator—a phenomenon that accounts for the precession of the equinoxes, the conical motion of the earth's axis, resembling a gyroscope. By studying the shape of the planet, furthermore, the possibility of estimating the length of day and night on the planet was shown.

Another application of the law of universal gravitation was Newton's exploration of the tides. When the moon is fullest, the earth's waters experience their maximum attraction, and high tide results. The sun also affects the tides, and when the sun and moon are in line, the tide is highest.

Still another subject of popular interest on which Newton shed light was comets. His theory was that comets, moving under the sun's attraction, travel elliptical paths of incredible magnitude, requiring many years to complete. Henceforth, comets, which were once regarded by the superstitious as evil omens, took their proper place as beautiful and harmless celestial phenomena. By using Newton's theories of comets, Edmund Halley was able to identify and to predict accurately the reappearance about every seventy-five years of the famous Halley's Comet. Once a comet has been observed, its future path can be accurately determined.

One of the most amazing discoveries made by Newton was his method for estimating the distance of a fixed star, based on the amount of light received by reflection of the sun's light from a planet.

The Principia made no attempt to explain the why but only the how of the universe. Later, in response to charges that his was a completely mechanistic scheme, making no provision for ultimate causes or for a Supreme Creator, Newton added a confession of faith to the second edition of his work.

This most beautiful system of the sun, planets, and comets could only proceed from the counsel and dominion of an intelligent and powerful Being.… As a blind man has no idea of colours, so have we no idea of the manner by which the all-wise God perceives and understands all things.

The function of science, he believed, was to go on building knowledge, and the more complete our knowledge is, the nearer are we brought to an understanding of the Cause, though man might never discover the true and exact scientific laws of nature.

Brilliant achievement that the Principia was, it was not written in a vacuum as Newton's most ardent admirers concede. I. Bernard Cohen stated:

The great Newtonian synthesis was based on the work of predecessors. The immediate past had produced the analytical geometry of Descartes and Fermat, the algebra of Oughtred, Harriot and Wallis, Kepler's law of motion, Galileo's law of falling bodies. It had also produced Galileo's law of the composition of velocities—a law stating that a motion may be divided into component parts, each independent of the other (for example the motion of a projectile is composed of a uniform forward velocity and a downward accelerated velocity like that of a freely falling body). The afore-mentioned are but a few of the ingredients present and waiting for the grand Newtonian synthesis. But it remained for the genius of Newton to add the master touch; to show finally, and once and for all, in just what manner the ordered universe is regulated by mathematical law.

It was evident that the world needed, as Sir James Jeans described Newton, "a man who could systematize, synthesize and extend the whole, and it found him in superlative excellence in Newton."

Newton himself recognized that his "System of the World," his mechanics of the universe, was built upon the work begun by Copernicus and so notably carried forward by Tycho Brahe, Kepler, and Galileo. "If I have seen farther than other men," Newton said, "it is by standing on the shoulders of giants."

In fact, the probable cause of the controversies that dogged Newton's life was the intellectual ferment prevailing in his time. The air was full of new theories, and many able scientists were exploring them. It is not surprising that two men would make the same discovery almost simultaneously and quite independently. Precisely this appears to have happened in Newton's two principal controversies, those with Leibniz and Hooke. Leibniz invented the differential calculus, and Hooke advanced a theory of universal gravitation, both somewhat later than Newton's, but announced to the world first, because Newton had neglected to publish his work.

The contemporary reception of the Principia was more cordial in England and Scotland than on the Continent, but everywhere slow. As Newton had foreseen, an understanding of it required great mathematical ability. The extraordinary nature of the performance was acknowledged, however, even by those who had only a dim conception of Newton's contribution. Gradually, scientists everywhere accepted the Newtonian system, and by the eighteenth century it was firmly established in the world of science.

After the Principia, Newton appears to have lost any active interest in scientific research, though he lived for forty years after its publication. During this period he was the recipient of many honors: he was appointed Master of the Mint, knighted by Queen Anne, elected President of the Royal Society from 1703 until his death in 1727, saw publication of the second and third editions of the Principia, and, in general, was held in the highest respect and esteem.

Scientific discoveries in the twentieth century have modified or shown inadequacies in Newton's work, especially in relation to astronomy. Einstein's theory of relativity, for example, maintains that space and time are not absolute, as Newton had taught. Nevertheless, as various authorities in science and technology have pointed out, the structure of a skyscraper, the safety of a railroad bridge, the motion of a motor car, the flight of an airplane, the navigation of a ship across the ocean, the measure of time, and other evidences of our contemporary civilization still depend fundamentally on Newton's laws. As Sir James Jean wrote, the Newtonian principles are "inadequate only with reference to the ultra-refinements of modern science. When the astronomer wishes to prepare his 'Nautical Almanac,' or to discuss the motions of the planets, he uses the Newtonian scheme almost exclusively. The engineer who is building a bridge or a ship or a locomotive does precisely what he would have done had Newton's scheme never been proved inadequate. The same is true of the electrical engineer, whether he is mending a telephone or designing a power station. The science of everyday life is still wholly Newtonian; and it is inipossible to estimate how much this science owes to Newton's clear and penetrating mind having set it on the right road, and this so firmly and convincingly that none who understood his methods could doubt their rightness.¹¹

The tribute paid Newton by Einstein should remove any question of rival philosophies: "Nature to him was an open book, whose letters he could read without effort. In one person he combined the experimenter, the theorist, the mechanic and, not least, the artist in expression."

Newton's own estimate of his career, made near the end of a long life, was characteristic of his modesty: "I do not know what I may appear to the world, but to myself I seem to have been only like a boy on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, while the great ocean of truth lay all undiscovered before me."