the improvement of the pendulum as a measure of time, and for some valuable innovations in the construction of pendulum watches, in particular the application of a spiral spring to regulate the balance. But in his own notion Hooke was the true author of several of the discoveries which have immortalised the greatest of his contemporaries. He disputed partly the originality, partly the truth, of Newton's theory of light; and he even asserted, when the Principia came out, that there was little or nothing there announced on the force and action of gravitation that he had not himself anticipated. He had, indeed, some years before, in a paper printed in the Philosophical Transactions, sketched an hypothesis of the movements of the earth and the other planets on the assumption of the principle of universal gravitation;* but this was a very different thing from the demonstration of the system of the world by Newton on the establishment and accurate measurement of that force. Newton himself eventually admitted that his proposition of the gravitation of the planets being as the inverse square of the distance had been previously deduced from Kepler's discovery of their elliptical orbits by Hooke, as well as by Wren and Halley; but this concession is supposed to have been made rather for the sake of peace than from conviction.

The first president of the Royal Society, William Brouncker, Lord Viscount Brouncker (of the kingdom of Ireland), who was born in 1620 and died in 1684, was an able mathematician, and is known as the author of the first series invented for the quadrature of the hyperbola, and also as the first writer who noticed what are called continued fractions in arithmetic. Dr. John Wallis (b. 1616, d. 1703) is the author of many works of great learning, ingenuity, and profoundness on algebra, geometry, and mechanical philosophy. Among the practical subjects to which he devoted himself were the deciphering of secret writing, and the teaching of persons born deaf to speak. "I was informed," says Sorbiere," that Dr. Wallis had brought a person that was born deaf and dumb to read at Oxford, by teaching him several inflections fitted to the organs of his voice, to make it articulate." The French traveller afterwards went to Oxford, and saw and conversed with Wallis (who held the office of Savilian Professor of Geometry in the university), although he

* Phil. Trans. No. 101 (for April, 1674).

Journey to England, p. 28.

complains that the professor and all the other learned Englishmen he met with spoke Latin, which was his medium of communication with them, with such an accent and way of pronunciation that they were very hard to be understood.* However, he adds that he was much edified, notwithstanding, by Wallis's conversation; and was mightily pleased both with the experiments he saw made by him in teaching the deaf to read, and with the model of a floor he had invented" that could bear a great weight, and make a very large hall, though it consisted only of several short pieces of timber joined together, without any mortices, nails, and pins, or any other support than what they gave one another; for the weight they bear closes them so together as if they were but one board, and the floor all of a piece." He gives a diagram of this ingenious floor; "and indeed," he continues, "I made Mr. Hobbes himself even admire it, though he is at no good terms with Dr. Wallis, and has no reason to love him." We have already mentioned the hot war, about what might seem the least heating of all subjects, that was carried on for some years between Wallis and Hobbes. A curious account is afterwards given of Wallis's personal appearance:- "The doctor," says our traveller, "has less in him of the gallant man than Mr. Hobbes; and, if you should see him with his university cap on his head, as if he had a porte-feuille on, covered with black cloth, and sewed to his calot, you would be as much inclined to laugh at this diverting sight as you would be ready to entertain the excellency and civility of my friend [Hobbes] with esteem and affection." And then the coxcomb adds—“ What I have said concerning Dr. Wallis is not intended in the least to derogate from the praises due to one of the greatest mathematicians in the world; and who, being yet no more than forty years of age [he was forty-seven], may advance his studies much farther, and become polite, if purified by the air of the court at London; for I must tell you, sir, that that of the university stands in need of it, and that those who are not purified otherways have naturally strong breaths that are noxious in conversation." It may be doubtful whether these last ex

66

*In this matter, "we do," says Spratt, in his answer, as all our neighbours besides; we speak the ancient Latin after the same way that we pronounce our mother tongue; so the Germans do, so the Italians, so the French," p. 159.

† Journey to England, p. 39.

Ibid. p. 41.

pressions are to be understood literally, or in some metaphorical sense; for it is not obvious 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 the great architect 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

* In No. 43, p. 867.

VOL. II.

M

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. 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 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