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151 [231] NEWTON
NEWTON [231] tween the mass of a body (representing its resistance to acceleration; or, in other words, the quantity of inertia it pos sessed) and its weight (representing the amount of gravitational force between it self and another body, usually the earth).
Finally the famous third law of mo tion states that for every action there is an equal and opposite reaction. That law makes news today, since it governs the behavior of rockets. Newton considered the behavior of moving bodies both in vacuum and in media that offered resis tance. In connection with the latter situa tion, he foreshadowed modem aeronau tics.
From the three laws Newton was able to deduce the manner in which the grav itational force between the earth and the moon could be calculated. He showed that it was directly proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between their centers. The proportionality could be made an equality by the introduction of a con stant. The equation that resulted is a fa mous one: Gmtm2 F —
c ? - where mx and m2 are the masses of the earth and the moon, d the distance be tween their centers, G the gravitational constant, and F the force of gravitational attraction between them. It was an additional stroke of tran scendent intuition that Newton main tained that this law of attraction held be tween any two bodies in the universe, so that his equation became the law of uni
endish [307] a century later to deter mine the value of G and, therefore, the mass of the earth, but Newton guessed that mass quite accurately and then es timated the mass of Jupiter and Saturn at nearly the correct value. It quickly became apparent that the law of universal gravitation was ex tremely powerful and could explain the motions of the heavenly bodies as they were then known. It explained all of Kepler’s laws. It accounted for the precession of the equinoxes. The various irregularities in planetary motions were seen to be the result of their minor at tractions (perturbations) for each other superimposed on the gigantic attraction of the sun. It even accounted for the complex variations in the motion of the moon. (This motion, which Kepler had not been able to deal with, was the only problem that Newton used to admit made his head ache.) Newton even in cluded a drawing in his book to illustrate the manner in which gravitation would control the motion of what we today call an artificial satellite. Newton’s great book was published in an edition of only twenty-five hundred copies, but it was well accepted and its value was recognized at once by many scientists. It represented the culmination of the Scientific Revolution that had begun with Copernicus [127] a century and a half earlier. Newton made the Scientific Revolution more than a matter of mere measurement and equations that theoretical philosophers might dismiss as unworthy to be compared with the grand cosmologies of the ancients. Newton had matched the Greeks at their grandest and defeated them. The
overall scheme of the universe, one far more elegant and enlightening than any the ancients had devised. And the New tonian scheme was based on a set of as sumptions, so few and so simple, devel oped through so clear and so enticing a line of mathematics that conservatives could scarcely find the heart and courage to fight it. It excited awe and admiration among Europe’s scholars. Huygens, for example, traveled to England for the ex press purpose of meeting the author. Newton ushered in the Age of Reason, during which it was the expectation of scholars that all problems would be solved by the acceptance of a few axioms worked out from careful observa tions of phenomena, and the skillful use of mathematics. It was not to prove to be as easy as all that, but for the eigh teenth century at least, man gloried in a new intellectual optimism that he had never experienced before and has never experienced since.
[231] NEWTON
NEWTON [231] Newton’s book, however, was not pub lished without trouble. The Royal Soci ety, which was to publish it, was short of funds and Hooke was at his most dispu tatious in claiming priority and pointing out he had written a letter to Newton on the subject six years earlier. Newton, brought to the extremes of exasperation, was finally forced (much against his rather ungenerous nature) to include a short passage referring to the fact that Hooke, Wren, and Halley had inferred certain conclusions that now Newton was to expound in greater detail. Even so the Royal Society, then under the presidency of none other than Samuel Pepys, the diarist, refused to involve it self in what might be a nasty controversy and backed out of its agreement to pub lish. Fortunately Halley, who was a man of means, undertook to pay all expenses of publication, arranged for illustrations, read galley proofs, and labored like a Trojan to keep Hooke quiet and New ton’s ever-sensitive nature mollified. When the book appeared, men of science rallied to the new view. David Gregory [240], the nephew of the man who had anticipated the reflecting telescope, was among the first. But continual controversy was wreak ing havoc with Newton, as was the terrific strain of his mental preoccu pations. (When asked by Halley how it was he made so many discoveries no other man did, Newton replied that he solved problems not by inspiration or by sudden insight but by continually think ing very hard about them until he had worked them out. This was no doubt true and if there were such a thing as mental perspiration, Newton must have been immersed in it. What’s more, he detested distractions and once scolded Halley for making a joking remark.) As though his work in mathematics and physics were not enough, Newton spent much time, particularly later in life, in a vain chase for recipes for the manufacture of gold. (He was an ardent believer in transmutation and wrote half a million worthless words on chemistry.) He also speculated endlessly on theolog ical matters and produced a million and a half useless words on the more mysti cal passages of the Bible. Like Kepler, he calculated the day of creation and set it about 3500 b .
., mak
ing the earth five centuries younger than Kepler had done. It was not till Hutton’s [297] time, a century later, that science was freed from enslavement to biblical chronology. Apparently Newton ended with Uni tarian notions that he kept strictly to himself, for he could not have remained at Cambridge had he openly denied the divinity of Christ. In any case in 1692 his busy mind tot tered. He had a nervous breakdown and spent nearly two years in retirement. His breakdown, according to a famous tale, may have been hastened by a mishap in which Newton’s dog Diamond upset a candle and burned years of accumulated calculation. “Oh, Diamond, Diamond,” moaned poor Newton, “thou little knowest the mischief thou hast done.” (Alas, this affecting story is probably not true. It is doubtful that Newton ever even owned a dog.) Newton was never quite the same, though he was still worth ten ordinary men. In 1696, for example, a Swiss mathematician challenged Europe’s schol- lars to solve two problems. The day after Newton saw the problems he for warded the solutions anonymously. The challenger penetrated the disguise at once. “I recognized the claw of the lion,” he said. In 1716, when Newton was seventy-five, a problem was set forth by Leibniz for the precise purpose of stumping him. Newton solved it in an af ternoon. In 1687 Newton defended the rights of Cambridge University against the un popular King James II, rather quietly, to be sure, but effectively. As a result he was elected a member of Parliament in 1689 after James had been overthrown and forced into exile. He kept his seat for several years but never made a speech. On one occasion he rose and the House fell silent to hear the great man. All Newton did was to ask that a win dow be closed because there was a draft. Through the misguided efforts of his friends he was appointed warden of the
[231] NEWTON
ROEMER [232] mint in 1696 with a promotion to master of the mint in 1699. This placed him in charge of the coinage at a generous sal ary, so that after his death he could leave an estate of over £.30,000. It was considered a great honor and only New ton’s due, but since it put an end to Newton’s scientific labors, it can only be considered a great crime. Newton re signed his professorship to attend to his new duties and threw himself into them with such vigor and intelligence that he revolutionized its workings for the better and became a terror to counterfeiters. He appointed his friend Halley to a posi tion under himself. In 1703 Newton was elected president of the Royal Society (only after Hooke’s death, be it noted) and he was reelected each year until his death. In 1704 he wrote Opticks, summarizing his work on light—having carefully waited for Hooke’s death here, too. Opticks, unlike the Principia, was written in English but it was soon translated into Latin so that Europeans outside Great Britain might read it. In 1705 he was knighted by Queen Anne. He had turned gray at thirty but his faculties remained sound into old age. At eighty he still had all his teeth, his eye sight and hearing were sharp, and his mind undimmed. Nevertheless, his duties at the mint neutralized this maintenance of vigor and prevented him from prepar ing a second edition of the Principia till 1713.
Newton was respected in his lifetime as no scientist before him (with the pos sible exception of Archimedes [47]) or after him (with the possible exception of Einstein [1064]). When he died he was buried in Westminster Abbey along with England’s heroes. The great French liter ary figure Voltaire [261], who was visit ing England at that time, commented with admiration that England honored a mathematician as other nations honored a king. The Latin inscription on his tomb ends with the sentence “Mortals! Rejoice at so great an ornament to the human race!” Even so, national prejudices had their influence and outside Great Britain there was some reluctance to accept the Newtonian system. It took a generation for it to win final victory. Newton had the virtue of modesty (or, if he did not, had the ability to assume it). Two famous statements of his are well known. He wrote, in a letter to Hooke in 1676, “If I have seen further than other men, it is because I stood on the shoulders of giants.” He also is sup posed to have said, “I do not know what I may appear to the world; but to myself I seem to have been only like a boy play ing on the seashore, and diverting myself in now and then finding a smoother peb ble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.” However, other men of Newton’s time stood on the shoulders of the same giants and were boys playing on the same sea shore, but it was only Newton, not an other, who saw further and found the smoother pebble. It is almost imperative to close any discussion of Newton with a famous couplet by Alexander Pope:
and with a verse by William Wordsworth who, on contemplating a bust of New ton, found it to be The marble index of a mind forever Voyaging through strange seas of thought, alone. [232] ROEMER, Olaus (roi'mer) Danish astronomer
25, 1644 Died: Copenhagen, September 19, 1710
Roemer, the son of a shipowner, stud ied astronomy at the University of Co penhagen under Bartholin [210], whom he also served as secretary; but his great achievement came in Paris. It seems that in 1671 the French astronomer Picard [204] traveled to Denmark in order to
[232] ROEMER
LEIBNIZ [233] visit the old observatory of Tycho Brahe [156], He wished to determine its exact latitude and longitude in order to recal culate if necessary Tycho’s observations of a century before. While there he uti lized the services of young Roemer as an assistant and impressed by him brought him back to Paris. In Paris, Roemer made his mark by carefully observing the motions of Ju piter’s satellites. Their times of revolu tion were accurately known, thanks to Cassini [209], another of Picard’s im ports. Because of this it was theoretically possible to predict the precise moment at which they would be eclipsed by Jupiter (as viewed from the earth). To Roemer’s surprise the eclipses came progressively earlier at those times of the year when the earth was ap proaching Jupiter in its orbit, and pro gressively later when it was receding from Jupiter. He deduced that light must have a finite velocity (though Aristotle [29] and, in Roemer’s own time, Des cartes [183] had guessed the velocity to be infinite) and that the eclipses were delayed when the earth and Jupiter were farthest apart because it took light sev eral minutes to cross the earth’s orbit. All previous attempts to determine the speed of light had failed. Galileo [166] had attempted to measure it by station ing an assistant on a hill with a lantern and himself on another hill with a lan tern and flashing lights back and forth. But the time lag between the flashing of one lamp and seeing the flash of the other in response seemed entirely due to the time it took a human being to react to a stimulus. There was no change in this lag when hills separated by greater distances were used. What Roemer had were two “hills” that were separated by some half a bil lion miles (earth and Jupiter) and a light flash (the moment of satellite eclipse) that did not involve human reac tion times. He calculated the velocity of light to be (in modem units) 227,000 ki lometers per second. Although this value is too small (the accepted modem value is 299,792 kilometers per second) it cer tainly was not bad for a first attempt. Roemer announced the calculation at a meeting of the Academy of Sciences in Paris in 1676. Although nowadays the velocity of light is considered one of the fundamental constants of the universe, this first announcement made no great splash. Picard backed his young protégé, as did Huygens [215], but the conser vative Cassini was opposed. In England, Halley [238], Flamsteed [234], and New ton [231] favored it, but on the whole the matter faded out of astronomical consciousness until Bradley [258] a half century later proved the finite velocity of light in a new and still more dramatic fashion. However, Roemer’s work in general was highly regarded. He visited England in 1679, meeting Newton, Flamsteed, and Halley, and in 1681 he was called back to Copenhagen by King Christian V to serve as astronomer royal and as professor of astronomy at the University of Copenhagen. There he reformed the Danish system of weights and measures and introduced the Gregorian calendar. In 1705 he was mayor of Copenhagen. The record of his extensive observa tions from Copenhagen was lost in 1728 in a fire that swept the city. [233] LEIBNIZ, Gottfried Wilhelm (lipe'nits) German philosopher and mathe matician
1646
Died: Hannover, November 14, 1716
Leibniz, the son of a professor of phi losophy who died when the boy was six, was an amazing child prodigy whose uni versal talents persisted throughout his life. Indeed, his attempt to do everything prevented him from being truly first class at any one particular thing. He has been called the Aristotle [29] of the seventeenth century and was perhaps the last to take—with reasonable success— all knowledge for his province. He began quite young, teaching him self Latin at eight and Greek at fourteen.
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FLAMSTEED [234] He obtained a degree in law in 1665 and, in addition, was a diplomat, philos opher, political writer, and an attempted reconciler of the Catholic and Protestant churches. As a diplomat he tried to dis tract Louis XIV from a prospective inva sion of Germany by suggesting a cam paign against Egypt instead. Louis XIV didn’t bite, but a century later Napoleon did. Leibniz also acted on occasion as adviser to Peter the Great, tsar of Rus sia. He was an atomist after the style of Gassendi [182] and tackled mathematics seriously after his travels brought him into contact with such men as Huygens [215] who introduced him to the mathe matical treatment of the pendulum. In 1671 he devised a calculating machine superior to that of Pascal [207], a ma chine that could multiply and divide as well as add and subtract. He was also the first to recognize the importance of the binary system of notation (making use of 1 and 0 only). (This is important in connection with modern computers.) Even earlier, in 1667, he had at tempted to work out a symbolism for logic. It was imperfect but it anticipated the work of Boole [595] two centuries later, in many ways. As a result, when Leibniz visited Lon don in 1673, where he met Boyle [212], he was elected a member of the Royal Society.
In that same year he began to think of a system of the calculus, which he pub lished in 1684. This eventually aroused a strenuous controversy between himself and the admirers of Newton [231], with Newton himself participating secretly. In fact, Newton all but accused Leibniz of plagiarism in the second edition of the Principia. Leibniz’s activity as a diplomat had been (of necessity) shady enough to make his word suspect to the furious Newtonians, and his contact with En glish mathematicians in 1673 seemed all the proof of plagiarism they needed. However, there seems no doubt now that his work was independent of Newton and, in any case, his line of development of the calculus was the superior. The ter minology and form first advanced by Leibniz is currently preferred to New ton’s. Leibniz also introduced the use of determinants into algebra. In 1693 he recognized the law of con servation of mechanical energy (the en ergy of motion and of position). A cen tury and a half later this was to be gen eralized by men such as Helmholtz [631] to include all forms of energy. Leibniz was also the first to suggest an aneroid barometer that would measure air pres sure against a thin metal diaphragm without the inconvenience of Torricelli’s [192] column of mercury. In 1700 Leibniz induced King Fred erick I of Prussia to match the Royal Society in London and the Academy of Sciences in Paris by founding the Acad emy of Sciences in Berlin and this has been a major scientific body ever since. Leibniz served as its first president. In 1700 also, he and Newton were elected (admirable neutrality of the French!) the first foreign members of the Parisian Academy of Sciences. For forty years Leibniz served the electors of Hannover. In 1710 Leibniz published, in French, a book in which he tried to demonstrate that this was the “best of all possible worlds” to use the now popular phrase. Surely, though, Leibniz must have found that hard to believe in his last few years, and after his death this view was mer cilessly satirized by Voltaire [261] in his
In 1714 the then elector of Hannover succeeded to the throne of Great Britain as George I, and Leibniz was eager to go with him to London. But the new king had no need of him and perhaps did not wish to offend the Newton partisans in his new kingdom. Leibniz died in Hannover, neglected and forgotten, with only his secretary at tending the funeral. Like his great adver sary, Newton, Leibniz had never married and had no family. [234] FLAMSTEED, John English astronomer
19, 1646 Died: Greenwich, near London, December 31, 1719 Download 17.33 Mb. Do'stlaringiz bilan baham: 
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