cused Leibnitz of having adopted the differential notation, in order to make it credible that he did not borrow his calculus from the writings of Newton.

› Leibnitz was irritated at this accusation, and called upon the Royal Society to interfere. A committee of that body was accordingly appointed to investigate the subject, and their report was published in 1712, under the title of "Commercium Epistolicum de Analysi promota." In this report, which makes a small octavo volume, the committee maintain that Leibnitz was not the first inventor, and they absolve Dr. Keill from all blame in giving the priority of the invention to Newton. They were, however, cautious in stating an opi nion upon that part of the charge in which Leibnitz was accused of plagiarism. John Bernoulli now entered the lists in behalf of his friend; but his arguments in defence of Leibnitz were too flimsy to obtain much credit, and it was generally allowed that Newton was the first inventor of the method of fluxions: and the real question is simply this,-Did Leibnitz see any of the writings of Newton that contained the principles of fluxions before he published in 1684 his "Nova Methodus pro maximis et minimis?" The friends of Leibnitz have adduced presumptive proofs that he had never seen the treatise of Newton "de Analysi," nor the Letter to Collins, in both of which the principles of the new calculus were to be found: and to strengthen their argument, they asserted that the writings already mentioned contained but a vague and obscure indication of the method of fluxions, and that Leibnitz or any one else might have perused them without having discovered it. Montucla, however, who will be regarded as impartial, or at least who cannot be suspected of partiality towards the English, has admitted that Newton in his treatise "de Analysi" has disclosed in a very concise and obscure manner his principles of fluxions, and that the suspicion of Leibnitz having seen this work is not destitute of probability: for Leibnitz admitted, that in his interview with Collins, he had seen a part of the epistolary correspondence between Newton and that gentleman. A more full account of this controversy may be found under the artib 2

cle

From

cle Keill in the Biographia Britannica. Dr. John Keill was born at Edinburgh in 1671. At the university of that city he was educated, and took his degree of M. A. whence he entered himself at Baliol college, Oxford. He is deserving of particular notice, as having been the first person who undertook to render the Newtonian philosophy popular, and to illustrate the profound theory, of sir Isaac by experiments. By this method he became early conversant with the Principia, and made himself master of a large portion of the immense treasure of mathematical and philosophi cal learning contained in that valuable but abstruse work. In 1698 he became more generally known by his "Examination of Dr. Thomas Burnet's Theory of the Earth," which was very well received. In 1701 he published his celebrated treatise entitled "Introductio ad Veram Physicam" this contained the substance of several lectures on the new philosophy, which he had the happy art of simplifying and of adapting to the faculty of young persons who had not gone very deeply into mathematical researches. It was at this period that he was on account of his superior merit elected a member of the Royal Society, and in 1708 he gave to that learned body a paper on the "Laws of Attraction and its physical Principles; a work that owed its foundation to certain propositions in sir Isaac Newton's Principia: of which he gives the following modest and unassuming account. "After frequently revolving in my mind the divine discoveries of this most sagacious man, I fell at last upon this thought, that a certain principle might be applied not unlike to those of Newton, to the explication of the terrestrial phænomena; and after experiments often repeated, I perceived there was a certain attractive force in terrestrial matter, from whence the reason of many terrestrial phænomena is to be derived: and this thought of mine about five years ago I opened to Mr. Newton, and I understood from him that he had long ago observed the same thing; and I found he had proposed some queries relating to this attractive force at the end of the Optics, published in Latin about two years ago. Now as it cannot be expected that this great man should proceed still to improve

improve these studies, both by reason of his age and other business, I thought it not amiss if I should pursue his steps herein, though at a great distance from him." This paper was published in the Philosophical Transactions, as was another by the same author, containing theorems on the rarity of matter, and the tenuity of its composition. In this paper he shows that a quantity of air, not bigger than the smallest grain of sand, may be diffused through the whole of Saturn, in such a manner as to leave therein no vacuity whose diameter shall exceed a given right line how small soever. This paper was drawn up as a sort of answer to Des Cartes's notion of a plenum but while our author was busy in vindicating his theory, her majesty queen Anne was pleased to appoint him her decipherer; and in the same year he was appointed Savilian professor of astronomy at Oxford. A short time after this he published his "Introductio ad veram Astronomiam," which he afterwards translated into English, and which was long a very popular book in the universities.

Among the mathematicians of this period must be noticed. Flamsteed, Halley, and Cotes. For Mr. Flamsteed the foundation of the Royal Observatory at Greenwich was laid, and he was the first resident as astronomer royal. It was, in honour of him, named Flamsteed-House, by which epithet it has ever since been known. Mr. Flamsteed was a clergyman, but never attained to any high degree of preferment. He had, however, learned of the religion which he taught, to be contented with a little. Through the whole course of his life he showed the most indefatigable assiduity in the prosecution of his labours for the improvement of astronomy; and the Transactions of the Royal Society afford clear evidences of his activity and diligence, as well as of his penetration and exactness. His principal work was partly printed off before his death; but it was not completed till 1725, when it was published and dedicated to King George I. This great work was entitled "Historia Coelestis Britannica." It consisted of three volumes folio, of which the first contained the observations of Mr. Gascoine, taken at Middleton in Yorkshire,

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Yorkshire, and those made by Mr. Flamsteed at Derby, between the years 1638 and 1643: also those made at the Royal Observatory between the years 1675 and 1689. The second volume contains his observations made with a capital telescope, on the zenith distances of the fixed stars, sun, moon, and planets, with their transits over the meridian; also notes and observations on the diameters of the sun and moon, with their eclipses, and those of Jupiter's satellites between the years 1689 and 1719. The third volume comprises a catalogue of the right ascensions, polar distances, longitudes and magnitudes of nearly 3000 fixed stars. The preface to this volume contains an account of all the astronomical observations made before his time, with a description of the instruments employed, and much other curious and highly important matter.

Dr. Halley was on account of his great scientific knowledge much employed by the queen. Scarcely had this princess ascended the throne than she sent him out to take a sur. vey of the ports of Dalmatia, with a view of forming a safe and convenient harbour for shipping in the Austrian territories on the Adriatic. He was on this occasion introduced to the emperor, to whom he gave an account of two harbours on the Istrian coast, and for which his majesty presented him with a valuable diamond ring, taken from his own finger, at the same time giving him a highly commendatory letter to the queen, written with his own hand. In 1703 he was appointed Savilian professor of geometry at Oxford, in the room of Dr. Wallis, which he held till he was appointed secretary to the Royal Society. He now undertook and completed a translation from the Arabic into Latin of "Apollonius de Sectione Rationis." He next prepared for the press "Apollonius's Conics," and subjoined to it the treatise of Serenus on the Section of the Cylinder and Cone." In 1708 he published his "Miscellanea Curiosa," in three volumes octavo, containing many original pieces of his own: and in 1719 he succeeded Mr. Flamsteed as astronomer-royal. In this situation he exerted all his powers in completing the theory

theory of the moon's motion, and in other observations on the heavens.

The only remaining mathematician which we shall notice as attaching to this period is Mr. Roger Cotes, who in 1699,* at the age of seventeen, was admitted pensioner of Trinitycollege, Cambridge, and in 1705 was chosen fellow of that college, being at the same time private tutor to the earl of Harold and his brother, the sons of the then marquis, afterwards duke of Kent. In the following year he was appointed professor of astronomy and experimental philosophy, upon the foundation made by Dr. Plume. For this office Mr. Cotes was not the only candidate, yet the votes were unanimously in his behalf. At the election, Mr. Whiston, who possessed considerable influence, said that he pretended himself to be not much inferior to Dr. Harris, the other candidate's master, but he confessed he was but a child to Mr. Cotes, who was then only in his 24th year. In 1713, at the desire of Dr. Bentley, he published a new edition of sir Isaac Newton's Principia, to which he prefixed a preface, which has been reprinted in all subsequent editions, whether issuing from British or foreign presses. Mr. Cotes in this preface, like the great author, endeavours to make the new philosophy subservient to rational piety and religion. In speaking of the advocates for a plenum, who maintain that the world was caused and existed not by the will of God, but by some necessity of nature, he says: "they will at last sink into the mire of that infamous herd, who dream that all things are governed by Fate and not by Providence." Having opposed this doctrine, he says:: "Without all doubt, this world so diversified with that variety. of forms and motions which we find in it, could arise from nothing but the perfectly free will of God directing and: presiding over all. From this fountain it is that those laws, which we call laws of nature, have flowed; in which there appear many traces indeed of the most wise contrivance, but not the least shadow of necessity." In reference to the Newtonian system and its author, he says: "To this method it is hardly to be said or imagined what

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light,