The Age of Louis XIV
Page 77
In 1666 he bought a prism at Stourbridge Fair, and began optical experiments. From 1668 onward he made a succession of telescopes. Hoping to avoid some defects persisting in the refracting telescope, he made with his own hands a reflecting telescope, on theorems set forth by Mersenne (1639) and James Gregory (1662), and presented it to the Royal Society at its request in 1671. On January 11, 1672, he was elected to membership in the Society.
Even before making telescopes he had reached (1666) one of his basic discoveries—that white light, or sunlight, is not simple or homogeneous, but is a compound of red, orange, yellow, green, blue, indigo, and violet. When he passed a small ray of sunlight through a transparent prism he found that the apparently monochrome light divided into all these colors of the rainbow; that each component color emerged from the prism at its own specific angle or degree or refraction; and that the colors arranged themselves in a row of bands, forming a continuous spectrum, with red at one end and violet at the other. Later investigators showed that various substances, when made luminous by burning, give different spectra; by comparing these spectra with the one made by a given star, it became possible to analyze in some degree the star’s chemical constituents. Still more delicate observations of a star’s spectrum indicated its approximate rate of motion toward or from the earth; and from these calculations the distance of the star was theoretically deduced. Newton’s revelation of the composition of light, and its refraction in the spectrum, has therefore had almost cosmic consequences in astronomy.
Hardly foreseeing these results, but feeling (as he wrote to Oldenburg) that he had made “the oddest if not the most considerable detection which hath hitherto been made in the operations of nature,” 18 Newton sent to the Royal Society early in 1672 a paper entitled “New Theory about Light and Colors.” It was read to the members on February 8, and aroused a controversy that crossed the Channel to the Continent. Hooke had described in his Micrographia (1664) an experiment similar to Newton’s with the prism; he had not deduced from it a successful theory of color, but he felt slighted by Newton’s ignoring his priority, and he joined with other members of the Society in criticizing Newton’s conclusions. The dispute lingered on for three years. “I am so persecuted,” wrote the thinskinned Newton, “with discussions arising out 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.” 19 For a time he was inclined to “resolutely bid adieu to philosophy eternally except what I do for my own satisfaction.” 20
Another point of controversy with Hooke concerned the medium through which light is transmitted. Hooke had adopted Huygens’ theory that light traveled on the waves of an “ether.” Newton argued that such a theory could not explain why light traveled in straight lines. He proposed instead a “corpuscular theory”: light is due to the emission, by a luminous body, of innumerable tiny particles traveling in straight lines through empty space with a speed of 190,000 miles per second. He rejected ether as a medium of light, but later accepted it as a medium of gravitational force.*
Newton gathered his discussions of light into the Opticks of 1704. Significantly, it was written in English (the Principia was in Latin), and was addressed “to Readers of quick Wit and Understanding not yet versed in Opticks.” At the end of the book he listed thirty-one queries for further consideration. Query I suggested prophetically: “Do not bodies act upon light at a distance, and by their action bend its rays, and is not this action strongest at the least distance?”† And Query XXX: “Why may not Nature change bodies into light, and light into bodies?”
III. THE GENEALOGY OF GRAVITATION
The year 1666 was germinal for Newton. It saw the beginning of his work in optics; but also, he later recalled, in May “I had entrance into the inverse method of Fluxions; and in the same year I began to think of gravity extending to the orbit of the moon, . . . having thereby compared the force requisite to keep the moon in her orbit with the force of gravity at the surface of the earth, and found them to answer pretty nearly. . . . In those years I was in the prime of my age.” 21
In 1666 the plague reached Cambridge, and for safety’s sake Newton returned to his native Woolsthorpe. At this point we come upon a pretty story. Wrote Voltaire, in his Philosophie de Newton (1738):
One day, in the year 1666, Newton, then retired to the country, seeing some fruit fall from a tree, as I was told by his niece, Mme. Conduit, fell into a profound meditation upon the cause which draws all bodies in a line which, if prolonged, would pass very nearly through the center of the earth. 22
This is the oldest known mention of the apple story. It does not appear in Newton’s early biographers, nor in his own account of how he came to the idea of universal gravitation; it is now generally regarded as a legend. More likely is another story in Voltaire: that when a stranger asked Newton how he had discovered the laws of gravitation, he replied, “By thinking of them without ceasing.” 23 It is fairly clear that by 1666 Newton had calculated the force of attraction holding the planets in their orbits as varying inversely with the square of their distance from the sun. 24 But he could not as yet reconcile the theory with his mathematical reckonings. He laid it aside, and published nothing about it for the next eighteen years.
The idea of interstellar gravitation was by no means original with Newton. Some fifteenth-century astronomers thought that the heavens exert a force upon the earth like that of the magnet upon iron, and that, since the earth is equally attracted from every direction, it remains suspended in the sum total of all these forces. 25 Gilbert’s De Magnete (1600) had set many minds thinking about the magnetic influences surrounding every body, and he himself had written, in a work that would be published (1651) forty-eight years after his death:
The force which emanates from the moon reaches to the earth, and, in like manner, the magnetic virtue of the earth pervades the region of the moon; both correspond and conspire by the joint action of both, according to a proportion and conformity of motions; but the earth has more effect, in consequence of its superior mass. 26
Ismaelis Bouillard, in his Astronomia philolaica (1645), had held that the mutual attraction of the planets varies inversely as the square of the distance between them. 27 Alfonso Borelli, in Theories of the Medicean Planets (1666), held “that every planet and satellite revolves round some principal globe of the universe as a fountain of virtue [force], which so draws and holds them that they cannot by any means be separated from it, but are compelled to follow it wherever it goes, in constant and continuous revolutions”; and he explained the orbits of these planets and satellites as the resultant of the centrifugal force of their revolution (“as we find in a wheel, or a stone whirled in a sling”) countered by the centripetal attraction of their sun. 28 Kepler considered gravity inherent in all celestial bodies, and for a while he reckoned its force as varying inversely with the square of the intervening distance; this would have clearly anticipated Newton; but later he rejected this formula, and supposed the attraction to be diminished in direct proportion as the distance increased. 29 These approaches to a gravitational theory were deflected by Descartes’ hypothesis of vortices forming in a primeval mass and then determining the action and orbit of each part.
Many of the alert inquirers in the Royal Society puzzled over the mathematics of gravitation. In 1674 Hooke, in An Attempt to Prove the Annual Motion of the Earth, anticipated by eleven years Newton’s announcement of the gravitation theory:
I shall explain a system of the world, differing in many particulars from any yet known, answering in all tilings to the common rules of mechanical motions. This depends upon three suppositions: first, that all celestial bodies whatsoever have an attractive or gravitating power towards their centers, whereby they attract not only their own parts, and keep them from flying from them, . . . but that they do also attract all other celestial bodies that are within the sphere of their activity. . . . The second suggestion is this, that all bodies whatsoever, that are put into direct a
nd simple motion, will so continue to move forward in a straight line, till they are by some other effectual powers deflected. . . . The third supposition is, that these attractive powers are so much the more powerful in operating, by how much nearer the body wrought upon is to their own centers. 30
Hooke did not, in this treatise, reckon the attraction as varying inversely with the square of the distance; but, if we may believe Aubrey, he communicated this principle to Newton, who had already arrived at it independently. 31 In January, 1684, Hooke propounded the formula of inverse squares to Wren and Halley, who themselves had already accepted it. They pointed out to Hooke that what was needed was no mere supposition, but a mathematical demonstration that the principle of gravitation would explain the paths of the planets. Wren offered to Hooke and Halley a reward of forty shillings ($100) if either would bring him, within two months, a mathematical proof of gravitation. So far as we know, none came. 32
Sometime in August, 1684, Halley went to Cambridge, and asked Newton what would be the orbit of a planet if its attraction by the sun varied inversely as the square of the distance between them. Newton replied, an ellipse. As Kepler had concluded, from his mathematical study of Tycho Brahe’s observations, that the planetary orbits are elliptical, astronomy seemed now confirmed by mathematics, and vice versa. Newton added that he had worked out the calculations in detail in 1679, but had laid them aside, partly because they did not fully accord with the then current estimates of the earth’s diameter and the distance of the earth from the moon; more probably because he was not sure that he could treat the sun, the planets, and the moon as single points in measuring their attractive force. But in 1671 Picard announced his new measurements of the earth’s radius and a degree of longitude, which last he calculated at 69.1 English statute miles; and in 1672 Picard’s mission to Cayenne enabled him to estimate the distance of the sun from the earth as 87,000,000 miles (the present figure is 92,000,000). These new estimates harmonized well with Newton’s mathematics of gravitation; and further calculations in 1685 convinced him that a sphere attracts bodies as though all its mass were gathered at its center. Now he felt more confidence in his hypothesis.
He compared the rate of fall in a stone dropped to the earth with the rate at which the moon would fall toward the earth if the gravitational pull of the earth upon the moon diminished with the square of the distance between them. He found that his results agreed with the latest astronomical data. He concluded that the force making the stone fall, and the force drawing the moon toward the earth despite the moon’s centrifugal impetus, were one and the same. His achievement lay in applying this conclusion to all bodies in space, in conceiving all the heavenly bodies as bound in a mesh of gravitational influences, and in showing how his mathematical and mechanical calculations tallied with the observations of the astronomers, and especially with Kepler’s planetary laws.*
Newton worked out his calculations anew, and communicated them to Halley in November, 1684. Recognizing their importance, Halley urged him to submit them to the Royal Society. He complied by sending the Society a treatise, Propositiones de Motu (February, 1685), which summarized his views on motion and gravitation. In March, 1686, he began a fuller exposition, and on April 28, 1686, he presented to the Society, in manuscript, Book I (De Motu Corporum) of Philosophiae Naturalis Principia Mathematica. Hooke at once pointed out that he had anticipated Newton in 1674. Newton answered, in a letter to Halley, that Hooke had taken the idea of inverse squares from Borelli and Bouillard. The dispute waxed to mutual irritation; Halley acted as peacemaker, and Newton soothed Hooke by inserting into his manuscript, under Proposition IV, a scholium in which he credited “our friends Wren, Hooke, and Halley” as having “already inferred” the law of inverse squares. But the dispute so irked him that when he announced to Halley (June 20, 1687), that Book II was ready, he added, “The third I now design to suppress. Philosophy is such an impertinently litigious lady that a man had as good be engaged in lawsuits as have to do with her.” Halley persuaded him to continue; and in September, 1687, the entire work was published under the imprint of the Royal Society and its current president, Samuel Pepys. The Society being short of funds, Halley paid for the publication entirely out of his own pocket, though he was not a man of means. So at last, after twenty years of preparation, appeared the most important book of seventeenth-century science, rivaled, in the magnitude of its effects upon the mind of literate Europe, only by the De revolutionibus orbium coelestium (1543) of Copernicus and The Origin of Species (1859) of Darwin. These three books are the basic events in the history of modern Europe.
IV. THE PRINCIPIA
The preface explained the title:
Since the ancients (as we are told by Pappus) made great account of the science of mechanics in the investigation of natural things; and the moderns, laying aside substantial forms [of the Scholastics] and occult qualities, have endeavored to subject the phenomena of nature to the laws of mathematics, I have in this treatise cultivated mathematics as far as it regards [natural] philosophy. . . . Therefore we offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena.
The viewpoint is to be strictly mechanical:
I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles, for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to that or some truer method of philosophy.
After laying down some definitions and axioms, Newton formulated three laws of motion:
1. Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.
2. The change of motion is proportional to the motive force impressed, and is made in the direction of the straight line in which that force is impressed.
3. To every action there is always opposed an equal reaction.
Armed with these laws, and the rule of inverse squares, Newton proceeded to formulate the principle of gravitation. Its current form, that every particle of matter attracts every other particle with a force varying directly as the product of their masses and inversely as the square of the distance between them, is nowhere found in these words in the Principia; but Newton expressed the idea in the general scholium that closes Book II: “Gravity . . . operates . . . according to the quantity of the solid matter which they [the sun and the planets] contain, and propagates its virtue on all sides, . . . decreasing always as the inverse square of the distances.” 33 He applied this principle, and his laws of motion, to the planetary orbits, and found that his mathematical calculations harmonized with the elliptical orbits deduced by Kepler. He argued that the planets are deflected from rectilinear motions, and are kept in their orbits, by a force tending toward the sun and varying inversely as the square of their distances from the center of the sun. On similar principles he explained the attraction of Jupiter upon its satellites, and of the earth upon the moon. He showed that Descartes’ theory of vortices as the first form of the cosmos could not be reconciled with Kepler’s laws. He calculated the mass of each planet, and figured the density of the earth as between five and six times that of water. (The current figure is 5.5.) He accounted mathematically for the flattening of the earth at the poles, and ascribed the bulge of the earth at the equator to the gravitational attraction of the sun. He worked out the mathematics of tides as due to the combined pull of the sun and the moon upon the seas; and by similar “lunisolar” action he explained the precession of the equi
noctial points. He reduced the trajectories of comets to regular orbits, and so confirmed Halley’s prediction. By attributing gravitational attraction to all planets and stars, he pictured a universe mechanically far more complex than had been supposed; for now every planet or star was viewed as influenced by every other. But into this complex multitude of heavenly bodies Newton placed law: the most distant star was subject to the same mechanics and mathematics as the smallest particles on the earth. Never had man’s vision of law ventured so far or so boldly into space.
The first edition of the Principia was soon sold out, but no second edition appeared till 1713. Copies became so scarce and hard to secure that one scientist transcribed the whole work with his own hand. 34 It was recognized as an intellectual enterprise of the highest order, but some notes of criticism soured the praise. France, clinging to Descartes’ vortices, rejected the Newtonian system until Voltaire gave it a worshipful exposition in 1738. Cassini and Fontenelle objected that gravitation was just one more occult force or quality; Newton propounded certain relationships among the heavenly bodies, but he had not revealed the nature of gravitation, which remained as mysterious as God. Leibniz argued that unless Newton could show the mechanism by which gravitation could act through apparently empty space upon objects millions of miles away, gravitation could not be accepted as anything more than a word. 35
Even in England the new theory was not readily received. Voltaire claimed that forty years after its first publication hardly twenty scientists could be found favorable to it. Whereas in France critics complained that the theory was insufficiently mechanical as compared with Descartes’ primeval whirlpools, in England the objections were predominantly religious. George Berkeley, in Principles of Human Knowledge (1710), regretted that Newton had thought of space, time, and motion as absolute, apparently eternal, and existing independently of divine support. Mechanism so pervaded the Newtonian system that there seemed no place in it for God.