communication with each other:-by Wren in this paper; by Wallis in another, read the preceding month; and by the celebrated Huyghens (who had been elected a fellow of the Society soon after its establishment), in a third, read in January, 1669. NEWTON. A greater glory is shed over this than over any other age in the history of the higher sciences by the discoveries of Sir Isaac Newton, the most penetrating and comprehensive intellect which has ever been exerted in that field of speculation. The era of Newton extends to the year 1727, when he died at the age of eighty-five. What he did for science almost justifies the poetical comparison of his appearance among men to the first dispersion of the primeval darkness at the creation of the material world : "God said, Let Newton be, and there was light." While yet in earliest manhood, he had not only outstripped and left far behind him the ablest mathematicians and analytic investigators of the day, but had discovered, it may be said, the whole of his new system of the world, except only that he had not verified some parts of it by the requisite calculations. The year 1664, when he was only twenty-two, is assigned as the date of his discovery of the Binomial Theorem; the year 1665 as that of his invention of fluxions; the year 1666 as that in which he demonstrated the law of gravitation in regard to the movement of the planets around the sun, and was only prevented from extending it to the movement of the moon around the earth, and to that of bodies falling towards the earth, by the apparent refutation of his hypothesis when attempted to be so applied, which was occasioned by the erroneous estimate then received of the earth's diameter. He did not attempt to wrest the supposed facts so as to suit his theory; on the contrary, with a singular superiority to the seductions of mere plausibility, he said nothing of his theory to any one, and seems even to have thought no more of it for sixteen years, till, having heard by chance, at a meeting of the Royal Society in 1682, of Picard's measurement of an arc of the meridian executed three years before, he thence deduced the true length of the earth's diameter, resumed and finished his long abandoned calculation--not without such emotion as compelled him to call in the assistance of a friend as he discerned the approaching confirmation of what he had formerly anticipated-and the following year transmitted to the Royal Society what afterwards formed the leading propositions of the Principia. That work, containing the complete exposition of the new theory of the universe, was published at London, at the expense of the Royal Society, in 1687. Meanwhile, about the year 1669, he had made his other great discovery of the non-homogeneity of light, and the differing refrangibility of the rays of which it is composed; by these fundamental facts revolutionising the whole science of optics. His Treatise on Optics, in which these discoveries and their consequences were developed, was first published in 1704; and along with it a Latin tract, entitled De Quadratura Curvarum, containing an exposition of the method of fluxions; of which, however, the Principia had already shown him to be in complete possession twenty years before, and which he had made use of in a paper written, according to his own account, in 1666, and undoubtedly communicated to Dr. Barrow, and by him to Mr. Collins, in 1669. This paper, entitled Analysis per Aequationes numero terminorum Infinitas, was published in 1711. question of the invention of the fluxionary or differential calculus, as is well known, gave occasion to a warm and protracted dispute between the partisans of Newton and those of his illustrious continental contemporary, Leibnitz; but it is now admitted on all hands, that, whatever claim Leibnitz also may have to be accounted its independent inventor (and there can scarcely be a doubt that he has a good claim to be so accounted), the honour of the prior invention belongs to Newton. The JAMES GREGORY, AND OTHER CONTEMPORARIES OF NEWTON. We must dismiss some other distinguished names with a very brief mention. James Gregory, who died in 1675 at the age of only thirty-six, after having been successively Professor of Mathematics at St. Andrews and at Edinburgh, had in his short life accomplished more than any of his contemporaries except Newton. He is popularly remembered chiefly as the inventor of the first reflecting telescope; but his geometrical and analytical inventions and discoveries were also numerous, and some of them of the highest order of merit. His nephew, David Gregory, Professor of Mathematics at Edinburgh, and afterwards Savilian Professor of Astronomy at Oxford, was also an able mathematician, and published some valuable works on geometry, optics, and astronomy. The Newtonian Theory of universal gravitation is said to have been taught by him at Edinburgh before it was introduced into any other European university. It is remarkable that when this David Gregory died, in 1708, he and two of his brothers held professorships in three British universities-himself at Oxford, James at Edinburgh, and Charles at St. Andrews. The last mentioned, too, was succeeded, upon his resignation in 1639, by his son, named David. 66 John Collins (b. 1624, d. 1683) is the author of several practical works and of a good many papers in the Philosophical Transactions; but he was most useful in promoting the publication of the works of others; it is said that Wallis's History of Algebra, Barrow's Optical and Geometrical Lectures, and various other publications owed their seeing the light principally to his instigation and encouragement. He also kept up an extensive epistolary intercourse with the other scientific men of the day it was principally from the letters and papers he left behind him that the Commercium Epistolicum, or volume of correspondence on the invention of fluxions, published in 1712, was made up Many of the discoveries in physical knowledge," says Dr. Hutton, "owe their chief improvement to him; for while he excited some to disclose every new and useful invention, he employed others in improving them. Sometimes he was peculiarly useful by showing where the defect lay in any branch of science, and pointing out the difficulties attending the inquiry; at other times explaining their advantages, and keeping up a spirit and energy for improvement. In short, Mr. Collins was like the register of all the new acquisitions made in the mathematical sciences; the magazine to which the curious had frequent recourse; which acquired him the appellation of the English Mersenne. Roger Cotes died in 1716, at the age of thirty-four, after having, in the estimation of his contemporaries, given promise of becoming one of the greatest mathematicians that had ever existed: Newton himself is reported to have said, "If Cotes had lived we should have known something.” Cotes's mathematical papers * Abridg. of Phil. Trans. i. 338. were published, in 1722, under the title of Harmonia Mensurarum, by his cousin Dr. Robert Smith (author of a work on optics), and his Hydrostatical and Pneumatical Lectures in 1738 by the same editor. Of all the publications that appeared in the early stages of the fluxionary calculus, Professor Playfair conceives that none is more entitled to notice than the Harmonia Mensurarum of Cotes. In this work, he observes, a method of reducing the areas of curves, in cases not admitting of an accurate comparison with rectilinear spaces, to those of the circle and hyperbola, which Newton had exemplified in his Quadratura Curvarum, was extended by Cotes, who also " gave the rules for finding the fluents of fractional expressions, whether rational or irrational, greatly generalised and highly improved by means of a property of the circle discovered by himself, and justly reckoned among the most remarkable propositions in geometry."* Another eminent authority describes the Harmonia as "the earliest work in which decided progress was made in the application of logarithms, and of the properties of the circle, to the calculus of fluents." Cotes superintended the printing of the second edition of Newton's Principia, published in 1713, and prefixed to it a preface which immediately acquired for him a wide scientific reputation. The last of these early English cultivators of the new calculus whom we shall mention is Dr. Brook Taylor, a geometrician and analyst of great profoundness and originality, whose Methodus Incrementorum, published in 1715, is characterised by Playfair as having "added a new branch to the analysis of variable quantity." "A single analytical formula," Playfair adds, "in the Method of Increments has conferred a celebrity on its author which the most voluminous works have not often been able to bestow. It is known by the name of Taylor's Theorem, and expresses the value of any function of a variable quantity in terms of the successive orders of increments, whether finite or infinitely small. If any one proposition can be said to comprehend in it a whole science, it is this: for from it almost every truth and every method of the new analysis may be deduced. It is difficult to say whether the theorem does most credit to the genius of the author, or the power of the language which is capable of concentrating such a vast body of knowledge in a * Dissertation on Progress of Math. and Phys. Science, p. 531. single expression.' Taylor's Theorem has since its first announcement been, in the language of the late Professor Leslie, "successively modified, transformed, and extended by Maclaurin, Lagrange, and Laplace, whose names are attached to their respective formulæ."† ESTABLISHMENT OF THE ROYAL OBSERVATORY. The example and discoveries of Newton, and especially the publication of the Principia, had, before the end of the seventeenth century, given a new direction and character to scientific speculation, and even to what was generally understood by the term science, in England. The day of little more than mere virtuosoship, in which the Royal Society had taken its rise and commenced its operations, had given place to that of pure science in its highest forms and most lofty and extensive applications. Next to the development and application of the fluxionary calculus, the field in which, as might have been expected, the impulse given by Newton produced the most brilliant results was that of astronomy. The Royal Observatory at Greenwich was founded by Charles II., for the benefit of astronomy and navigation, in 1676; and the appointment of Astronomer Royal (or Astronomical Observator, in the official style) bestowed upon John Flamsteed, then about thirty years of age, and already distinguished as a cultivator of astronomical science. Flamsteed held this office till his death in 1719; and during that space of time made and published a voluminous series of observations, from the commencement of which his late biographer Mr. Baily dates the commencement of modern astronomy. "Nor," observes another writer, to whose masterly contributions to the history of the mathematical sciences we have been repeatedly indebted in the preceding pages, "can such chronology be disputed, if we consider that we now return to Flamsteed's observations as the earliest with which it is desirable to compare those of our day, and also that Flamsteed's Catalogue is the first which attained a precision comparable to that of later times." What is here * Dissertation, p. 532. † Dissertation on the Progress of the Math. and Phys. Sciences in the Eighteenth Century, in Encyclopædia Britannica, p. 599. Article on Flamsteed, in Penny Cyclopædia, x. 296. |