THE PIONEERING OBSERVATIONS AND NEW THEORIES OF COPERNICUS, Tycho Brahe, Kepler, and Galileo, together with those of some of their contemporaries, represent part of an intellectual upheaval that came to be called the Scientific Revolution, which continued through the seventeenth century and on into the early years of the eighteenth, a period during which the worldview of western Europe changed profoundly and modern scientific culture emerged.
Some historians today take issue with the concept of a Scientific Revolution, as historian and sociologist Steven Shapin remarked in his definitive work on the subject:
Many historians are now no longer satisfied that there was any singular and discrete event, localized in time and space, that can be pointed to as “the” Scientific Revolution. Such historians now reject even the notion that there was even any single coherent entity called “science” in the seventeenth century to undergo revolutionary change. There was, rather, a rather diverse array of cultural practices aimed at understanding, explaining and controlling the natural world, each with different characteristics and each experiencing different modes of change. We are now much more dubious of claims that there is anything like a “scientific method”—a cultural, universal, and efficacious set of procedure for making scientific knowledge—and still more skeptical of stories that locate its origins in the seventeenth century, from which time it has been unproblematically passed on to us.
One particularly influential system of natural philosophy that emerged in the seventeenth century was mechanism, which held that all natural phenomena was due to one single kind of change, the motion of matter. The approach of the mechanistic philosophy of nature is broadly summarized by Pierre Gassendi (1592–1565), a French Catholic priest who in 1647 published a work in which he attempted to reconcile the atomic theory with Christian doctrine. “There is no effect without a cause; no cause acts without motion, nothing acts on distant things except through itself or an organ or transmission; nothing moves unless it is touched, whether directly or through an organ or through another body.”
Gassendi’s mechanism was based on the atomic theory as interpreted by Lucretius, in which physical properties are traced to the imagined size and shape of the component particles. Gassendi was deeply influenced by Isaac Beeckman (1566–1637), who expressed his corpuscular form of mechanism in the statement that “all properties arise from [the] motion, shape and size [of the fundamental particles]. So that each of these three things must be considered.”
A number of different approaches to scientific investigation were formulated in the seventeenth century. One was the empirical, inductive method proposed by Francis Bacon (1561–1626); another was the theoretical, deductive approach of René Descartes (1596–1650).
According to Bacon, the new science should be based primarily on observation and experiment, and it should arrive at general laws only after a careful and thorough study of nature. In his Novum organum, published in 1620, Bacon criticized the existing state of scientific knowledge. “The subtlety of nature greatly exceeds that of sense and understanding, so that those fine meditations, speculations and fabrications of mankind are unsound, but there is no one to stand by and point it out. And just as the sciences we now have are useless for making discoveries of practical use, so the present logic is useless for the discovery of the sciences.”
Bacon never accepted the Copernican theory, which he called a hypothesis, and he criticized both Ptolemy and Copernicus for presenting nothing more than “calculations and predictions” rather than “philosophy … what is found in nature herself, and is actually and really true.”
Descartes sought to give physical laws the same certitude as those of mathematics. As he wrote in a letter to Marin Mersenne: “In physics I should consider that I knew nothing if I were able to explain only how things might be, without demonstrating that they could not be otherwise. For having reduced physics to mathematics, this is something possible, and I think that I can do it within the small compass of my knowledge, though I have not done it in my essays.”
Descartes writes of how he proposed to himself four “laws of reasoning,” which he applied first to the study of mathematics:
In this way I believed I could borrow all that was best both in geometrical analysis and in algebra, and correct all the defects of the one by the help of the other. And, in points of fact, the accurate observance of these few precepts gave me such ease in unraveling all the questions embraced in these two sciences, that in the two or three months I devoted to their examination, not only did I reach solutions of questions I had formerly deemed exceedingly difficult, but even as regards questions of the solutions of which I remained ignorant, I was enabled as it appeared to me, to determine the means whereby, and the extent to which, a solution was possible.
Whereas in philosophy Descartes began with the existence of self (Cogito ergo sum, I am thinking, therefore I exist), in physics he started with the existence of matter, its extension in space, and its motion through space. That is, everything in nature can be reduced to matter in motion. Matter exists in discrete particles that collide with one another in their ceaseless motions, changing their individual velocities in the process, but with the total “quantity of motion” in the universe remaining constant. Descartes wrote of the divine origin of this law in his Principles of Philosophy (1644), an extraordinarily detailed and elaborate model of the physical universe based on his corpuscular mechanistic theory. Speaking of God, he said, “In the beginning, in his omnipotence, he created matter, along with its motion and rest, and now, merely by his regular concurrence, he preserves the same amount of motion and rest in the material universe as he put there in the beginning.”
Descartes presented his method in Rules for the Direction of the Mind, completed in 1628 but not published until after his death, and in the Discourse on Method, published in 1637 along with appendices entitled Optics, Geometry, and Meteorology. He gave the final form of his three laws of nature in The Principles of Philosophy (1644). The first law, the principle of inertia, states that “each and every thing, insofar as it can, always continues in the same state, and thus what is once in motion always continues to move.” The second law, dealing with directionality, states that “all motion is in itself rectilinear … every piece of matter, considered in itself, always tends to continue moving, not in any oblique path but only in a straight line.” The third law is concerned with collisions: “If a body collides with another body that is stronger than itself, it loses none of its motion; but if it collides with a weaker body, it loses a quantity of motion equal to that which it imparts to the other body.”
The Optics presents Descartes’ mechanistic theory of light, which he conceived of as a series of impulses propagated through the finely dispersed microparticles that fill the spaces between macroscopic bodies, leaving no intervening vacuum. This model gave him the right form for the law of refraction, but in his derivation he took the velocity of light to be greater in water than in air, which is not true.
The Geometry was inspired by what Descartes called the “true mathematics” of the ancient Greeks, particularly Pappus and Diophantus. Here he provided a geometric basis for algebraic operations, which to some extent had already been done by his predecessors as far back as al-Khwarizmi. The symbolic notation used by Descartes quickly produced great progress in algebra and other branches of mathematic. His work gave rise to the branch of mathematics now known as analytic geometry, which had been anticipated by Pierre Fermat (1539–1565). Fermat, inspired by Diophantus and Apollonius, was also one of the founders of modern number theory and probability theory.
Descartes’ Meteorology includes his model of the rainbow, in which he used the laws of reflection and refraction to obtain the correct values of the angles at which the primary and secondary bows appear. He begins his explanation by pointing out that rainbows occur not only in the sky but also in illuminated fountains and sprays, so that it is not solely a celestial phenomenon but rather one involving light and individual drops of water. He tested this hypothesis by taking a spherical glass flask full of water, holding it up at arm’s length in the sunlight, and moving it up and down so that colors are produced. He says that if he stood with his back to the sun so as to let the light come
from the part of the sky marked AFZ and my eye be at E, then when I put this sphere at the place BCD the part of it at D seems to me wholly red and incomparably more brilliant than the red. And whether I move toward it or step back from it, and move to the right or the left, or even turn it in a circle around my head, the provided the line DE always makes an angle of around 42° with the line EM, which one must imagine to extend from the center of the eye to the center of the sun, D always appears equally red. But as soon as I made the angle DEM the slightest bit larger, the redness disappeared. And when I made it a little bit smaller it did not disappear completely in one stroke but first divided as into two less brilliant parts in which could be seen yellow, blue and other colours. Then, looking towards the place marked K on the sphere, I perceived that, making the angle KEM around 52°, K also appeared to be colored red, but not as brilliant as D.
Then, using a sheet of black paper to screen off selected parts of the sunlight, Descartes determined the path of the rays producing the various colors of both the primary and secondary rainbows. He concluded, as had Dietrich of Freiburg, that the primary rainbow was produced by two refractions and one internal reflection within each of the raindrops, while the secondary bow was generated by two refractions and two internal reflections, the second of which had the effect of inverting the spectrum.
Descartes’ model of the rainbow
Descartes then performed several experiments to show that the actual dispersion of light into colors was due only to refraction and not reflection. In one of these experiments he dispersed sunlight in a glass prism and observed the colors on a screen. When sunlight strikes the face perpendicularly, it passes through the glass to a narrow aperture in the darkened base, where it is refracted and dispersed into a band HGF on the screen, with violet appearing above, red below, and the other colors in between. He then tried to explain why the dispersion takes place and “why these colors are different above and below, even though the refraction, shadow and light concur there in the same way.” The explanation that he proposed was an extremely detailed mechanistic model based on his microcorpuscular theory of matter. One of the assumptions that Descartes had made in this theory is that light travels more rapidly in dense media such as water and glass than in air, which is incorrect.
Chapters 8 through 12 of Descartes’ Le monde present his mechanistic cosmology, based on his theory of matter and laws of motion. This hypothetical “new world” that he described consisted of an indefinite number of contiguous vortices, each with a star at its center. He argued that the stars were the sources of light just like our sun, for “if we consider how bright and glittering the rays of the fixed stars are, despite the fact that they are an immense distance from the sun, we will not find it hard to accept that they are not like the sun. Thus if we are as close to one of them as we are to the sun, that star would in all probability appear as large and luminous as the sun.” He held that each of these stars is the center of a planetary system, all carried around by the motion of the particles of the three types of matter that he believed filled all of space.
Descartes’ vortex theory was generally accepted at first, but the research of Christiaan Huygens (1629–1695) showed conclusively that it was completely incorrect. Huygens was led to his rejection of the vortex theory by his studies of dynamics. In one of his studies he considered a situation in which a lead ball is attached to a string held by a man standing at the center of a rotating platform. When the platform rotates the man feels an outward or centrifugal force in the string attached to the ball, which in turn experiences an inward or centripetal force due to the string. Huygens found that the centripetal force on the ball was directly proportional to the mass of the ball and the square of its velocity, and inversely proportional to the radius of its circular path, thus establishing the basis of dynamics for circular motion. This and his researches on the laws of collisions were what led Huygens to conclude that the Cartesian cosmology was in error. As he said in 1693, he could find “almost nothing I can approve as true in all the physics and metaphysics” of Descartes.
Huygens found that Descartes’ rules concerning collisions were not mutually consistent. Descartes held there was both relativity of motion and conservation of motion, while Huygens realized that these are incompatible with each other. He saw that his task was to clarify just what relativity of motion implied for collisions.
In his De motu corporum ex percussione, the first version of which was completed in the mid-1550s, Huygens framed an ingenious thought experiment, carried out by two men, one of them in a boat moving at constant speed along a canal and the other standing on the shore. The man in the boat has two identical metal spheres attached by strings from his outstretched hands, which he brings together to make them collide elastically just as he passes the man on the shore, who joins hands with him at that moment, so that they are in effect doing the experiment together. If the boat is moving at the same speed as one of the bodies, then the man on the shore will see a moving body colliding with one at rest, the latter being given a velocity equal to that which the former had before collision. The man on the boat, on the other hand, sees the two bodies as simply interchanging their velocities. All other cases involving the collisions of two identical bodies can be accommodated to this symmetrical case simply by changing the speed of the boat.
By looking at the same phenomenon in two different frames of reference, Huygens showed that the center of gravity of a system is unchanged in an elastic collision. That is, if the center of gravity is at rest, as it is for the man on the shore, then it will remain at rest despite the collision, whereas if it is moving with constant speed, as it is for the man in the boat, then it will continue to do so.
Huygens also did pioneering work on motion in his treatise on the pendulum clock, the Horologium oscillilatorium, published in 1673. The thesis describes an isochronus pendulum clock invented by Huygens in 1656, in which the pendulum bob swings against a cycloidal surface, which makes its period independent of amplitude for all angles. Huygens describes the significance of his research, noting that “the simple pendulum does not naturally provide an accurate and equal measure of time since the wider motions are observed to be slower than the narrower ones. But by a geometrical method we have found a different and previously unknown way to suspend the pendulum; and we have discovered a line whose curvature is marvelously and quite rationally suited to give the required equality to the pendulum.”
Huygens’ demonstration of the relativity of motion
Part 2 of the Horologium begins with three hypotheses on dynamics. The first, which is a clear statement of the principle of inertia, states that in the absence of gravity a body will continue in any motion it already has in a straight line at constant velocity. The second hypothesis is that gravity always acts so as to impose a downward component on any uniform motion the body has, and the third says that these motions are independent of one another.
Descartes’ Aristotelian notion that a vacuum was impossible was also shown to be incorrect by several of his contemporaries, beginning with Evangelista Torricelli (1608–1647) and Blaise Pascal (1623–1662). Torricelli’s invention of the barometer in 1643 led him to conclude that the closed space above the mercury column represented at least a partial vacuum, and that the difference in the height of the two columns in the U-tube was a measure of the weight of a column of air extending to the top of the atmosphere. Pascal had a barometer taken to the top of the Puy de Dôme, a peak in central France, and it was observed that the difference in height of the two columns was less than at sea level, verifying Torricelli’s conclusions. The results of this experiment led Pascal to urge all disciples of Aristotle to see if the writings of their master could explain the results. “Otherwise,” he wrote, “let them recognize that experiments are the real masters that we should follow in physics; that the experiment done in the mountains overturns the universal belief that nature abhors a vacuum.”
The German engineer Otto von Guericke (1602–1680) discovered that it was possible to pump air as if it were water, allowing him to produce a vacuum mechanically. In a famous experiment in Magdeburg in 1657, he pumped the air out of a spherical cavity made by fitting together two copper hemispheres and showed that the resulting differential pressure was so great that not even two teams of horses pulling in opposite directions could force the two halves of the sphere apart.
Guericke’s demonstration led the Irish chemist Robert Boyle (1627–1691) to have a vacuum pump constructed by the instrument maker Ralph Greatorex. The design of the pump was subsequently improved by the English physicist Robert Hooke (1635–1703). Boyle fitted the pump with a Torricellian barometer and noted the change in the level of mercury as the tube was evacuated. He then used the pump to do research on pneumatics, which he published in 1660 under the title New Experiments Physico-Mechanicall, Touching the Spring of Air and Its Effects. He concluded that a vacuum can be produced, or at least a partial one; that sound does not propagate in a vacuum; and that air is necessary for life or a flame. Additionally, air is an elastic fluid that exerts a pressure against whatever restricts it and expands when it is relieved of external constraints: “Air ether consists of, or at least abounds with, parts of such a nature, that in case they be bent or compress’d by the incumbent part of thermosphere, they do endeavour, as much as in them lies, to free themselves from that pressure, by bearing upon the contiguous bodies that keep them bent.” In an appendix to the second edition of this work, published in 1662, he established the relationship now known as Boyle’s law, that the pressure exerted by a gas is inversely proportional to its volume.
Boyle was influenced by both Francis Bacon’s empiricism and Descartes’ mechanistic view of nature. He was also influenced by the natural philosophy of Epicurus, revived by Pierre Gassendi. This led Boyle to adopt a divinely ordained corpuscular version of mechanism, which he described in his treatise on Some Thoughts About the Excellence and Grounds of the Mechanical Philosophy, published in 1674. As he concluded concerning the universality of mechanism: “By this very thing that the mechanical principles are so universal, and therefore applicable to so many other things, they are rather fitted to include, than necessitated to exclude, any other hypothesis, that is founded in nature, as far as it is so.”
The scientific developments that had taken place from the time of Copernicus through that of Galileo culminated with the career of Isaac Newton (1642–1727), whose supreme genius made him the central figure in the emergence of modern science.
Newton was born on December 25, 1642, in the same year that Galileo had died. His birthplace was the manor house of Woolsthorpe in Lincolnshire, England. His father, an illiterate farmer, had died three months before Isaac was born, and his mother remarried three years later, though she was widowed again after eight years. When Newton was twelve he was enrolled in the grammar school at the nearby village of Grantham, and he studied there until he was eighteen. His maternal uncle, a Cambridge graduate, sensed that his nephew was gifted and persuaded Isaac’s mother to send the boy to Cambridge, where he was enrolled at Trinity College in June 1661.
At Cambridge Newton was introduced to Aristotelian science and cosmology as well as the new physics, astronomy, and mathematics of Copernicus, Kepler, Galileo, Fermat, Descartes, Huygens, and Boyle. In 1663 he began studying under Isaac Barrow (1630–1677), the newly appointed Lucasian professor of mathematics and natural philosophy. Barrow edited the works of Euclid, Archimedes, and Apollonius, and published his own works on geometry and optics, with the assistance of Newton.
Isaac Newton, 1702
By Newton’s own testimony, he began his researches in mathematics and physics late in 1664, shortly before an outbreak of plague closed the university at Cambridge and forced him to return home. During the next two years, his anni mirabilis, he began his research in calculus and the dispersion of light, and discovered his law of universal gravitation and motion as well as the concepts of centripetal force and acceleration.
In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, and in November had the direct method of fluxions & the next year in January had the Theory of Colours & in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with which [a] globe revolving within a sphere presses the surface of the sphere) from Keplers rule of the periodic times of the Planets being sesquialternate proportion of their distances from the center of their Orbs. I deduced that the forces which keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force required to keep the Moon in her Orb with the force of gravity at the surface of the earth & found them answer pretty nearly. All this was in the two plague years 1665 and 1666 for in those years I was in the prime of my age for invention & minded Mathematicks & Philosophy more than at any time since.
This indicates that Newton had derived the law for centripetal force and acceleration by 1666, some seven years before Huygens, though he did not publish it at the time. He applied the law to compute the centripetal acceleration at the earth’s surface caused by its diurnal rotation, finding that it was less than the acceleration due to gravity by a factor of 250, thus settling the old question of why objects are not flung off the planet by its rotation. He computed the centripetal force necessary to keep the moon in orbit, comparing it to the acceleration due to gravity at the earth’s surface, and found that they were inversely proportional to the squares of their distances from the center of the earth. Then, using Kepler’s third law of planetary motion together with the law of centripetal acceleration, he verified the inverse square law of gravitation for the solar system. At the same time he laid the foundations for calculus and formulated his theory for the dispersion of white light into its component colors.
In the spring of 1667, when the plague subsided, Newton returned to Cambridge. Two years later he succeeded Barrow as Lucasian professor of mathematics and natural philosophy, a position he was to hold for nearly thirty years.
During the first few years after he took up his professorship, Newton devoted much of his time to research in optics and mathematics. He continued his experiments on light, examining its refraction in prisms and thin glass plates as well as working out the details of his theory of colors. He built a reflecting telescope with a magnifying power of nearly forty, and then made a refractor that he claimed magnified 150 times, using it to observe planets and comets. The latter telescope came to the attention of the Royal Society, which elected him a Fellow on January 11, 1672.
As part of his obligations as a Fellow, Newton wrote a paper on his optical experiments, which he submitted on February 28, 1672, to be read at a meeting of the Society. The paper, subsequently published in the Philosophical Transactions of the Royal Society, described his discovery that sunlight is composed of a continuous spectrum of colors, which can be dispersed by passing light through a refracting medium such as a glass prism. He found that the “rays which make blue are refracted more than the red,” and he concluded that sunlight is a mixture of light rays, some of which are refracted more than others. Furthermore, once sunlight is dispersed into its component colors it cannot be further decomposed. This meant that the colors seen on refraction are inherent in the light itself and are not imparted to it by the refracting medium.
The paper was characteristic of Newton’s attitude toward the approach to be followed in any scientific investigation. Later, in a controversy arising out of his first paper, Newton described his scientific method.
For the best and safest method of philosophizing seems to be, first to enquire diligently into the properties of things, and to establish these properties by experiment, and then to proceed more slowly to hypotheses for the explanation of them. For hypotheses should be employed only in explaining the properties of things, but not assumed in determining them, unless so far as they may furnish experiments.
Ironically, the paper was widely criticized by Newton’s contemporaries for just the contrary reason: that it did not confirm or deny any general philosophy of nature, and the mechanists objected that it was impossible to explain his findings on the basis of any mechanical principles. Then there were others who insisted that Newton’s experimental findings were false, since they themselves could not find the phenomena that he had reported. Newton replied patiently to each of these criticisms in turn, but after a time he began to regret ever having presented his work in public.
One of those who criticized his paper was Robert Hooke, who in November 1662 been had been appointed as the first curator of experiments at the newly founded Royal Society, a position he held until his death in 1703, making many important discoveries in mechanics, optics, astronomy, technology, chemistry, and geology. His lengthy critique of the paper seemed to imply that Hooke had performed all of Newton’s experiments himself, while rejecting the conclusions that Newton had drawn.
This led Newton to resign from the Royal Society early in 1673, but Henry Oldenburg, secretary of the Society, refused to accept his resignation and persuaded him to remain. Then in 1676, after a public attack by Hooke, Newton broke off almost all association with the Oldenburg and the Royal Society. The following year Oldenburg died and Hooke replaced him as secretary, whereupon he wrote a conciliatory letter in which he expressed his admiration for Newton. Referring to Newton’s theory of colors, Hooke said that he was “extremely well pleased to see those notions promoted and improved which I long since began, but had not time to compleat.”
Newton replied in an equally conciliatory tone, referring to Descartes’ work on optics. “What Descartes did was a good step. You have added much several ways, and especially in taking the colors of thin plates into philosophical consideration.”
But despite these friendly sentiments, the two were never completely reconciled, and Newton maintained his silence. Nevertheless they continued to communicate with each other, a correspondence that was to lead again and again to controversy, the bitterest dispute arising from Hooke’s claim that he had discovered the law of gravitation before Newton.
By 1684 others beside Hooke and Newton were convinced that the gravitational force was responsible for holding the planets in their orbits and that this force varied with the inverse square of their distance from the sun. Among them were the astronomer Edmund Halley (1656–1742), a good friend of Newton’s and a fellow member of the Royal Society. Halley made a special trip to Cambridge in August 1684 to ask Newton what he thought the curve would be that would be described by the planets supposing the force of attraction toward the sun to be reciprocal to the square of their distance from it. Newton replied immediately that it would be an ellipse, but he could not find the calculation, which he had done seven or eight years before. And so he was forced to rework the problem, after which he sent the solution to Halley that November.
By then Newton’s interest in the problem had revived, and he developed enough material to give a course of nine lectures in the fall term at Cambridge, under the title of De motu corporum (The Motion of Bodies). When Halley read the manuscript of De motu he realized its immense importance, and he obtained Newton’s promise to send it to the Royal Society for publication. Newton began preparing the manuscript for publication in December 1684 and sent the first book of the work to the Royal Society on April 28, 1686.
On May 22, Halley wrote to Newton saying that the Society had entrusted him with the responsibility for having the manuscript printed. But he added that Hooke, having read the manuscript, claimed that it was he who had discovered the inverse square nature of the gravitational force and thought that Newton should acknowledge this in the preface. Newton was very much disturbed by this, and in his reply to Halley he went to great lengths to show that he had discovered the inverse square law of gravitation and that Hooke had not contributed anything of consequence.
The first edition of Newton’s work was published in midsummer 1687 at the expense of Halley, since the Royal Society had found itself financially unable to fund it. Newton entitled his work Philosophicae naturalis principia mathematica (The Mathematical Principles of Natural Philosophy), referred to more simply as the Principia. The Principia begins with an ode dedicated to Newton by Halley. This is followed by a preface in which Newton outlines the scope and philosophy of his work.
Our present work sets forth mathematical principles of natural philosophy. For the basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions, and then to demonstrate the other phenomena from these forces.… Then the motions of the planets, the comets, the moon, and the sea are deduced from these forces by propositions that are also mathematical. If only we could derive the other phenomena of nature from mechanical principles by the same kind of reasoning!
Book 1 begins with a series of eight definitions, of which the first five are fundamental to Newtonian dynamics. The first effectively defines “quantity of matter,” or mass, as being proportional to the weight density times volume. The second defines “quantity of motion,” subsequently to be called “momentum,” as mass times velocity. In the third definition Newton says that the “inherent force of matter,” or inertia, “is the power of resisting by which every body, so far as it is able, perseveres in its state either of rest or of moving uniformly straight forward.” The fourth states that “impressed force is the action exerted upon a body to change its state either of resting or of uniformly moving straight forward.” The fifth through eighth define centripetal force as that by which bodies “are impelled, or in any way tend, toward some point as to a center.” As an example Newton gives the gravitational force of the sun, which keeps the planets in orbit.
As regards the gravity of the earth, he gives the example of a lead ball, projected from the top of a mountain with a given velocity, and in a direction parallel to the horizon. If the initial velocity is made larger and larger, he says, the ball will go farther and farther before it hits the ground, and may go into orbit around the earth or even escape into outer space.
The definitions are followed by a scholium, a lengthy comment in which Newton gives his notions of absolute and relative time, space, place, and motion. These essentially define the classical laws of relativity, which in the early twentieth century would be superseded by Einstein’s theories of special and general relativity.
An illustration from Newton’s Principia, showing a projectile in orbit around the Earth.
Next come the axioms, now known as Newton’s laws of motion, three in number, each accompanied by an explanation and followed by corollaries.
Law 1: Every body perseveres in its state of being at rest, or of moving uniformly forward, except insofar as it is compelled to change its state of motion by forces impressed.
Law 2: A change of motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.
Law 3: To every action there is always an opposite and equal reaction; in other words, the action of two bodies upon each other are always equal, and always opposite in direction.
The first law is the principal of inertia, which is actually a special case of the second law when the net force is zero. The form used today for the second law is that the force F acting on a body is equal to the time rate of change of the momentum p, where p equals the mass m times the velocity v; if the mass is constant then F = ma, a being the acceleration, the time rate of change of the velocity. The third law says that when two bodies interact, the forces they exert on each other are equal in magnitude and opposite in direction.
The introductory section of the Principia is followed by book 1, entitled “The Motion of Bodies.” This begins with an analysis of motion in general, essentially using calculus. First Newton analyzed the relations between orbits and central forces of various kinds. From this he was able to show that if and only if the force of attraction varies as the inverse square of the distance from the center of force, then the orbit is an ellipse, with the center of attraction at one focal point, thus proving Kepler’s second law of motion. Elsewhere in book 1 he proves Kepler’s first and third laws. He also uses his third law of motion to deal with problems involving two bodies mutually attracting each other, where he notes that neither of the two bodies can be considered to be at rest: “For attractions are always directed toward bodies, and—by the third law—the actions of attracting and attracted bodies are always mutual and equal; so that if there are two bodies, neither the attracting and attracted body can be at rest, but both … revolve around a common center of gravity as if by mutual attraction.”
Book 2 is also entitled “The Motion of Bodies,” for the most part dealing with forces of resistance to motion in various types of fluids. One of Newton’s purposes in this analysis was to see what effect the hypothetical aether in Descartes’ cosmology would have on the motion of the planets. His studies showed that the Cartesian vortex theory was completely erroneous, for it ran counter to the laws of motion in resisting media that he established in book 2 of the Principia.
The third and final book of the Principia is entitled “The System of the World,” beginning with three “Rules for the Study of Natural Philosophy.” After this comes a section on “Phenomena,” six in number, followed by forty-two propositions, each accompanied by a theorem and lemmas, sometimes followed by a scholium. This is in turn followed by a general scholium and a concluding section entitled “The System of the World.”
The six phenomena concern the motion of the planets and the earth’s moon, along with observations concerning Kepler’s second and third laws of planetary motion. He concludes that the planets, “by radii drawn to the center …, describe areas proportional to the times, and their periodic times—the fixed stars being at rest—are as the 3/2 powers of their distances from that center.”
The various propositions and lemmas are concerned with the consequences of Newton’s theory for both terrestrial and celestial motion. His law of universal gravitation states that “gravity exists in all bodies universally and is proportional to the quantity of matter in each.” It also states that the gravitational force between two bodies varies as the inverse square of the distance between their centers of mass. This inverse-square gravitational force explains the motion of the planets orbiting the sun, the satellites of Jupiter, and the earth’s moon, as well as the local gravity on the earth itself. Proposition 13 states Kepler’s first and second laws of planetary motion: “The planets move in ellipses that have a focus in the center of the sun, and by radii drawn to that center they describe areas proportional to the times.”
Telescopic observation of the planets had revealed that they were oblate spheres, as stated in proposition 18: “The axes of the planets are smaller than the diameters that are drawn perpendicular to the axes,” that is, the planets are oblate spheres. Newton correctly attributed this effect to the centrifugal forces arising from the axial rotation of the planets, so that the earth, for example, is flattened at the poles and bulges around the equator.
Newton’s theory of tidal action, is stated in proposition 24: “The ebb and flow of the sea arises from the actions of the sun and moon,” finally solving a problem that dated back to the time of Aristotle. Another ancient problem is stated in proposition 39: “Find the precession of the equinoxes,” including the gravitational forces of both the sun and the moon on the earth. Newton correctly computed that “the precession of the equinoxes is more or less 50 seconds [of arc] annually,” thus solving another problem that had preoccupied astronomers for some two thousand years.
Still another ancient unsolved question is settled in lemma 4, which states that “the comets are higher than the moon, and move in the planetary regions.” In the lemmas and propositions that follow, Newton discusses the motion of comets, showing that they move in elliptical orbits around the sun, thus reappearing periodically, as did the one known as Halley’s comet, which had been observed in 1682 after disappearing seventy-five years before. He also speculated on the nature of comets, saying, as had Kepler, that the tail of a comet represents vaporization from the comet’s head as it approaches the sun.
This is followed by a general scholium, in which Newton says that mechanism alone cannot explain the universe, whose harmonious order indicated to him the design of a Supreme Being. “This most elegant system of the sun, planets, and comets could not have arisen without the design and dominion of an intelligent and powerful being.”
A second edition of the Principia was published in 1713 and a third in 1726, in both cases with a preface written by Newton. Meanwhile in 1704 Newton had published his research on light, much of which had been done early in his career. Unlike the Principia, which was in Latin, the first edition of his new work was in English, entitled Opticks, or a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light. The first Latin edition appeared in 1706, and subsequent English editions appeared in 1717/1718, 1721, and 1730; the last, which came out three years after Newton’s death, bore a note stating that it was “corrected by the author’s own hand, and left before his death, with his bookseller.”
Like the Principia, the Opticks is divided into three books. At the very beginning of book 1 Newton reveals the purpose he had in mind when composing his work. “My design in this Book,” he writes, “is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiment.”
The topics dealt with in book 1 include the laws of reflection and refraction, the formation of images, and the dispersion of light into its component colors by a glass prism. Other topics include the properties of lenses and Newton’s reflecting telescope; the optics of human vision; the theory of the rainbow; and an exhaustive study of color. Newton’s proof of the law of refraction is based on the erroneous notion that light travels more rapidly in glass than in air, the same error that Descartes had made. This error stems from the fact that both of them thought that light was corpuscular in nature.
Newton’s corpuscular view of light stemmed from his acceptance of the atomic theory. He wrote of his admiration for “the oldest and most celebrated Philosophers of Greece … who made a Vacuum, and Atoms, and the Gravity of Atoms, the first Principles of their Philosophy.… All these things being consider’d, it seems to me that God in the Beginning formed Matter in solid, hard, impenetrable, moveable Particles, of such Sizes and Figures, and with such other Properties and in such Proportions to Space, as much conduced to the End for which he had form’d them.”
Book 2 begins with a section entitled “Observations Concerning the Reflexions, Refractions, and Colours of Thin Transparent Bodies.” The effects that he studied here are now known as interference phenomena, where Newton’s observations are the first evidence for the wavelike nature of light.
In book 2 Newton also comments on the work of the Danish astronomer Olaus Roemer (1644–1710), who in 1676 measured the velocity of light by observing the time delays in successive eclipses of the Jovian moon Io as Jupiter receded from the earth. Roemer’s value for the velocity of light was about a fourth lower than the currently accepted one of slightly less than 300,000 kilometers (186,410 miles) per second, but it was nevertheless the first measurement to give an order of magnitude estimation of one of the fundamental constants of nature. Roemer computed that light would take eleven minutes to travel from the sun to the earth, as compared to the correct value of eight minutes and twenty seconds. Newton seems to have made a better estimate of the speed of light than Roemer, for in book 2 of the Opticks he says that “Light is propagated from luminous Bodies in time, and spends about seven or eight Minutes of an Hour in passing from the Sun to the Earth.”
In book 3 the opening section deals with Newton’s experiments on diffraction. The remainder of the book consists of a number of hypotheses, not only on light, but on a wide variety of topics in physics and philosophy. The first edition of the Opticks had sixteen of these queries, the second twenty-three, the third and fourth forty-one each. It would seem that Newton, in the twilight of his career, was bringing out into the open some of his previously undisclosed speculations, his heritage for those who would follow him in the study of nature.
Meanwhile Newton had been involved in a dispute with the great German mathematician and philosopher Gottfried Wilhelm Leibniz (1646–1716), the point of contention being which of them had been the first to develop calculus. According to his own account, Newton first conceived the idea of his “method of fluxions” around 1665–1666, although he did not publish it until 1687, when he used it in the Principia. He first published his work on calculus independently in a treatise that came out in 1711. Leibniz began to develop the general methods of calculus in 1675, though he did not publish his work until 1684. The version of calculus formulated by Leibniz, whose notation was much like that used today, caught on more rapidly than that of Newton, particularly on the Continent. Newton’s bitterness over the dispute was such that in the third edition of the Principia he deleted all reference to Leibniz, who until the end of his days continued to accuse his adversary of plagiarism.
Aside from his work in science, Newton also devoted much of his time to studies in alchemy, prophecy, theology, mythology, chronology, and history. His most important nonscientific work is Observations upon the Prophecies of Daniel, and the Apocalypse of St. John, which is considered to be a possible key to the method of his alchemical studies, as evidenced by such notions as his analogy between the “four metals” of alchemy and the four beasts of the apocalypse.
In 1689 Newton was elected by the constituency of Cambridge University to serve as member of Parliament. He was made warden of the mint in March 1696, whereupon he appointed William Wiston as his deputy in the Lucasian professorship at Cambridge. He finally resigned his professorship on March 10, 1710, shortly after his second election as MP for the university. He was knighted by Queen Anne at Trinity College on April 16, 1705; on May 17, 1706, he was defeated in his third campaign for the university’s seat in Parliament.
Newton died in London on March 20, 1727, four days after presiding over a meeting of the Royal Society, of which he had been president since 1703. His body lay in state until April 4, when he was buried with great pomp in Westminster Abbey. The baroque monument marking his tomb shows Newton in a reclining position, along with a weeping female figure, representing Astronomy, Queen of the Sciences, sitting on a globe above. The inscription on the tomb concludes with: “Let Mortals rejoice That there has existed such and so great an Ornament to the Human Race.”
His contemporaries hailed Newton’s achievement as the perfection of the mechanistic philosophy of nature, and historians of the mid-twentieth century praised his work as the culmination of the Scientific Revolution. Although many historians of the new millennium now take issue with the notion of a Scientific Revolution, it is generally agreed that Newton’s work culminated the long development of European science, creating a synthesis that opened the way for the scientific culture of the modern age.
Newton himself paid tribute to his predecessors when he said, in response to Hooke, “If I have seen further than Descartes, it is by standing on the sholders [sic] of Giants.” Newton was echoing the statement that had made five centuries earlier by Bernard Silvestre.
Bernard was writing just before the founding of the first of the new European universities, opening up Graeco-Islamic science and philosophy to Latin Europe. Thus the predecessors he was referring to were the scholarly monks who had toiled away obscurely in the monasteries of Ireland and England and then on the Continent, studying the scraps of classical learning that had survived the collapse of the Graeco-Roman world and trying to understand the world around them, cultivating the nascent scientific tradition that would come to fruition with the works of Copernicus, Kepler, Galileo, and Newton.
Newton himself was referring not only to his European predecessors, but also to the ancient Greek philosophers and scientists from Thales and Pythagoras and the other pre-Socratics through Democritus, Plato, Aristotle, Euclid, Archimedes, Apollonius, Aristarchus, Eratosthenes, and Ptolemy, whose manuscripts had been lost in the burning of the great Library of Alexandria, the lost knowledge slowly recovered in medieval Byzantium, the Middle East, and Europe until finally, more than twelve centuries later, it gave rise to the Newtonian synthesis that began modern science.
Newton himself was referring not only to his European predecessors but also to the ancient Greek philosophers and scientists from the Presocratics up through the Hellenistic period, whose manuscripts had been destroyed in the burning of the great Library of Alexandria, the lost knowledge slowly recovered and further developed in medieval Byzantium, Islam and Europe, paving the way for the Newtonian synthesis.
Beginning a thousand years before Galileo, with one thinker passing on ideas to another, enlightenment gradually dispelled the darkness and led to the dawning of the modern scientific age.