The discoveries of Sir Isaac Newton (b. 1642; d. 1727), however, put the crown to the glories of this period. Their extent can only be learnt by a perusal of his "Principia; or, Mathematical Principles of Natural Philosophy," containing his complete theory of the laws of the universe, based on the grand doctrine of Gravitation, of which he published afterwards a popular view under the title of "De Mundi Systemate," enunciating the truths contained in the third book of the "Principia;" his "Optics," containing his theories of light and colour, founded on a host of curious experiments; his "De Quadratura Curvarum," containing an exposition of his method of fluxions; his "Method of Fluxions and Analysis by Infinite Series." A great many of those discoveries were made known to the public through his communications to the Royal Society. The announcement of his binomial theorem, by which he was able to determine the area and rectification of curves, the surface and contacts of the solids formed by their revolution and the position of their centre of gravity—a theory of infinite avail in his determination of the laws of the planetary bodies—is dated 1664, that of his "Method of Fluxions," 1665; but he did not claim this till 1669. He professed to have written a tract on the subject in 1664, but he did not produce this tract till he had seen some of the same results published in Mercator's "Logarithmotechnia," four years afterwards. In 1666 he demonstrated the great law of gravitation, and applied it to the planets, but was baffled in his attempts to apply it to the moon through a false estimate of the earth's diameter. This was corrected by Picard's measurement of an arc of the meridian, with which Newton became acquainted in 1682, and then after sixteen years' delay he completed his system. But his "Principia" was not published collectively till 1687; his "Optics" till 1704, with his "De Quadratura Curvarum."
Unparalleled as were the achievements of Newton, these were not accomplished, any more than any other great performances, without substantial hints and assistance from preceding or contemporary genius. The very principle of gravitation had been pointed out by Robert Hooke, and Newton was compelled to admit, and offered to publish a scholium acknowledging the fact, that Hooke, Wren, and Halley had already deduced this law—that the gravitation of the planets was as the curvic square of the distance—from Kepler's second law of analogy between the periodic times and the mean distances of the planets. Newton's defenders say that he probably made this concession for the sake of peace; but was Newton likely to surrender a great truth, vitally affecting his fame for science and discovery, if there were not solid grounds for it?
Still less to the credit of Newton was his conduct towards Leibnitz in the dispute regarding the Differential Calculus. Leibnitz having heard through Oldenburg that Newton had made discoveries as to the measurement of tangents, in fact, as to his binomial theorem, and as to fluxions, desired to have some account of them, and Newton, through Oldenburg, communicated to Leibnitz his binomial theorem, but concealed his knowledge of fluxions under a most abstruse anagram, which was formed from the words, "Data Equatione quotcunque fluentes quantitates envolvente fluxiones invenire, et vice versâ." It has been well observed that if Leibnitz could draw any light from that anagram, he must have possessed superhuman sagacity. Leibnitz, however, having himself made most important discoveries in fluxions, at once and candidly communicated the theory of what he called, and what is still called, the differential calculus, to Newton. This, Newton, in a scholium included in his "Principia," admitted to be a method hardly differing from his own except in the form of words and symbols. Yet in the third edition of the "Principia" he omitted this confession, claimed the exclusive invention of the differential calculus for himself, and branded Leibnitz as a plagiarist. The fact was, that Leibnitz had gone a step beyond Newton. Newton had discovered fluxions, but Leibnitz had discovered the fluxionary calculus, or, as he termed it, the differential calculus.
Still more discreditable was the conduct of Newton to Flamsteed (b. 1646; d. 1719). Flamsteed was the first Astronomer Royal. Charles II. established an observatory at Greenwich, one of the best things he ever did. The observatory was, in fact, the queen's house in Greenwich Park, and Flamsteed was appointed Astronomical Observator, with the magnificent salary of a hundred pounds a year, and not a single instrument, not even a telescope. It was in vain that he applied for instruments; and his appointment might have been a sinecure had he not procured instruments at his own expense, and taught pupils to maintain himself. But through all these difficulties he went on making observations, and in time not only made a mass of the most valuable lunar observations, but had made a map and catalogue of the stars, such as there had never been before for completeness and accuracy. His catalogue included three thousand three hundred stars, "whose places were more accurate than any determined in the next fifty years, and whose selection and nomenclature has served as a basis to every catalogue since that time." Bailey, Flamsteed's biographer, claims—and very justly claims—that the commencement of modern astronomy dates from his observations, for no one would care to go beyond them to compare any made in our day.
Newton was very intimate with Flamsteed, and with good cause, for he depended on his supplying him with the necessary observations to enable him to establish his lunar theory, and it is on evidence that Flamsteed furnished him with every lunar observation that he made. When Flamsteed had completed his catalogue, he proposed to publish it, and Prince George of Denmark, knowing that Flamsteed had expended on his instruments two thousand pounds more than his salary, offered to pay for the printing. A committee, consisting of Newton, Sir Christopher Wren, Dr. Arbuthnot, Dr. Gregory, and Mr. Roberts, was appointed to superintend this publication. The whole story, based on letters and documents of the time found at Greenwich observatory, is too long to be detailed here; but the upshot of it is, that the catalogue and observations of Flamsteed were printed and published, not as his own, but as those of Halley. In vain did Flamsteed protest against this most scandalous deed. Newton and his associates were strong in the favour of the queen and Halifax, and Newton used the most opprobrious language to the man by whose labours he had so greatly benefited, and whom he had now helped to rob of his dearest possession—his fame. The softest name that he gave him was that of "puppy." Flamsteed could obtain no redress—though they had broken his seal to come at his catalogue—till after the death of Queen Anne and Halifax, when he was enabled to get possession of the remainder of the books called Halley's, styled, "Historia Celestis libri duo." He immediately began preparations for publishing them himself, and demanded his MSS. from Newton, who refused, and was sued for them by Flamsteed. In the meantime, to avoid being compelled to give up the MSS. to the rightful owner, Newton handed them over to Halley! Every insult was offered to Flamsteed. He was summoned before the Royal Society to answer whether he had his instruments in order, a matter in which the Society had no authority, and what made the matter more atrocious, the instruments were Flamsteed's own. Newton even twitted Flamsteed with his one hundred pounds a year salary, at which Flamsteed indignantly reminded him that he had been receiving three hundred pounds a year himself ever since he came to London. Flamsteed's work was not completed till after his death, when it appeared under the name of "Historia Cœlestis Britannica."
It is difficult to conceive more overbearing, unjust, and unworthy proceedings than those of Newton against Flamsteed. Sir David Brewster, in his "Life of Newton," endeavoured to defend him by asserting that Flamsteed did not appreciate Newton's theory; as if Flamsteed was not quite at liberty to have his own opinion, an opinion shared by many at the time, and which theory, in the first edition of the "Principia," the only one then out, was in some respects grossly incorrect—"rejected," as Flamsteed remarked, "by the heavens." Brewster also urged that Flamsteed showed unwillingness to furnish Newton with the requisite lunar observations. He was under no obligation whatever to do so; yet, as proved, he furnished him with all he had made. It is contended also that the committee had a right to break the seal of Flamsteed to get at his catalogue—an assertion than which nothing can be more immoral.
On the whole view of this case, as it rests on broad facts, we are compelled, in justice between man and man, to declare our opinion that Flamsteed was not only one of the most illustrious astronomers which England has ever produced, but also one of the most ill-used of men; and without derogating an iota from the scientific merits of Sir Isaac Newton, it is clear, from his conduct to both Leibnitz and Flamsteed, that he adds another proof to that of Bacon, that intellectual greatness and moral greatness do not necessarily reside in the same mind.
Amongst the other men of mathematical note in this period we may mention Henry Briggs, the coadjutor of Napier. His "Trigonometrica Britannica" showed that he had had a near view of the binomial theorem afterwards discovered by Newton. This work was published after his death by his friend, Henry Gellibrand, also an able mathematician. Thomas Harriott, author of a work on algebra—"Artis Analyticæ Praxis"—is said to have discovered the solar spots before Galileo, and the satellites of Jupiter only a few days after Galileo. Jeremiah Horrocks was beforehand with Newton in the theory of the lunar motions, which Newton afterwards demonstrated to be the necessary consequence of gravitation. Dr. Wallis, Crabtree, Gascoigne, Milbourn, Shakerley, and Gunter—the author of Gunter's Scale—were all men of high merit in those branches of science. Barrow we have already mentioned as a distinguished geometrician as well as a theologian. He was only excelled in optics by Newton himself; and in his "Sectiones Geometricæ" he nearly anticipated Newton's principle of fluxions. James Gregory, professor of mathematics at Edinburgh, the first constructor of a reflecting telescope; and his nephew, David Gregory, of Oxford; John Collins, author of various philosophical works and papers; Roger Cotes, author of "Harmonia Mensurarum," etc.; and Dr. Brook Taylor, author of "Methodus Incrementorum," were all substantial contributors to the higher sciences at this era. Halley, whose name occurs so unfavourably in the affair with Flamsteed, succeeded him as Astronomer Royal, and is noted as being the first to find out the exact return of a comet which bears his name, and for his catalogue of the southern stars, published in 1679. Besides his profound astronomical talents, he added in various ways to the knowledge of the time. He was the first to construct tables of mortality; introduced improvements in the diving-bell; and wrote treatises on the variations of the compass, on the trade winds, and other subjects.
SIR ISAAC NEWTON.