how the air of a court, though it may polish a man's address, is actually to sweeten a bad breath. Dr. Wallis, besides his publication of the papers of Horrocks already noticed, edited several of the works of Archimedes, Ptolemy, and other ancient mathematicians; and he is also the author of a Grammar of the English tongue, written in Latin, which abounds in curious and valuable matter. Another ingenious though somewhat fanciful mathematician of this day was Dr. John Wilkins, who was made Bishop of Chester some years after the Restoration, although during the interregnum he had married a sister of Oliver Cromwell, as Archbishop Tillotson had a niece in the reign of Charles I. Dr. Wilkins is chiefly remembered for his' Discovery of a New World,' published in 1638, in which he attempts to prove the practicability of a passage to the moon; and his Essay towards a Real Character,' being a scheme of a universal language, which he gave to the world thirty years later. He is also the author of various theological works. Of the high mathematical merits of Dr. Isaac Barrow we have already spoken. Barrow's Lectiones Opticæ, published in 1669, and his Lectiones Geometricæ, 1670, contain his principal contributions to mathematical science. The former advanced the science of optics to the point at which it was taken up by Newton: the latter promulgated a partial anticipation of Newton's differential calculus-what is known by the name of the method of tangents, and was the simplest and most elegant form to which the principle of fluxions had been reduced previous to the system of Leibnitz. Barrow's Mathematica Lectiones, not published till after his death, which took place in 1677, as already mentioned, at the early age of forty-six, are also celebrated for their learning and profoundness. Another person who likewise distinguished himself in this age by his cultivation of mathematical science, although he earned his chief renown in another department, was Sir Christopher Wren. Wren's most important paper in the Philosophical Transactions is one on the laws of the collision of bodies, read before the Royal Society in December, 1668.* It is remarkable that this subject, which had been recommended by the society to the attention of its members, was at the same time completely elucidated by three individuals working without communication with each other:-by Wren in this paper; by Wallis in another, read the preceding month; and by the celebrated Huygens (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 out* In No. 43, p. 867. stripped 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 -- Meanwhile, expense of the Royal Society, in 1687. 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 æquationes numero terminorum infinitas,' was published in 1711. The 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. 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 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. 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, |