there is not a word either "in commendation or discommendation." Their fate was to be very little noticed at the time; for after they had been several years in the world, he heard of only two men who had given them a careful perusal, Slusius of Liege, and James Gregory in Scotland. The latter had seen the Lectiones Optica, and writes thus to Collins" Mr. Barrow in his Opticks sheweth himself a most subtil geometer, so that I think him superior to any that ever I looked upon. I long exceedingly to see his Geometrical Lectures, especially because I have some notions upon that subject by mee. I entreat you to send them to mee presently, as they come from the presse, for I esteem the author more than yee can imagine." Though he could not but be gratified with the approbation of such a man, he could not afford to publish for so select a circle of readers; and the general neglect of such subjects tended to produce in his own mind a dissatisfaction with the science itself. For though his edition of Apollonius, &c. appeared subsequently to his Optics, it had been prepared for the press before them; and with the publication of the latter work he seems to have taken leave of mathematics altogether. He resigned the chair in 1669, and at his own request was succeeded by his favourite pupil, the immortal Newton. The value of Barrow's mathematical labours has been underrated by some recent writers. The following is the fairest estimate of their importance which we remember to have met with :-"His Lectiones Geometrica are filled with profound investigations respecting the properties of curvilineal figures; and in the method of tangents which he has explained in that work, we clearly discover the germ of the fluxional calculus. This ingenious method, which is a great simplification of the rule given by Fermat, differs in nothing but the notation, from the method of finding the subtangent by the Differential Calculus. The Optical Lectures of Dr. Barrow are distinguished by the same original views which characterize his Lectures on Geometry. His beautiful theory of the apparent place of objects seen by refraction or reflection, and the elegant determinations which he has given of the form of the images of rectilineal objects received from mirrors and lenses, entitle him to the highest praise. By pushing these researches a little farther, Barrow could not fail to have discovered the caustic or Tschirnhausenian curves."* To this we add the service which he rendered to mathematical science by restoring the works of some of its great fathers. To publish improved editions of Euclid, Archimedes, Apollonius, and Theodosius, should of itself have procured for Barrow a place of note in the history of mathematical learning. But he had a still more original merit in the improvements which he introduced into the language of geometry. He discarded many of the cumbrous circumlocutions which had been considered essential to the ancient strictness, and by a judicious employment of symbols did much to promote its perspicuity. At the same time he had too high veneration for the approved methods of antiquity, to substitue in their place the notation which then began to prevail. For this he was often commended by Newton.* After all, it is frivolous to be disputing about the extent of Barrow's mathematical acquirements. His fame does not rest on the fact of his having held two geometrical professorships in succession-of his having been admired by the greatest mathematicians of the day-of his having been the tutor and predecessor of Newton. It rests on his works, and these are such that we do not know any one throughout the whole of the last century who ever doubted his pretensions. Even those who had not sense enough to understand his Sermons, allowed that he was a mathematician.† Montucla, who called him a poor philosopher because he believed in the immortality of the soul and the existence of God, is full of "admiration" and " enchantment" when he speaks of the fertility of ideas and the multitude of new and curious theorems "de ce savant géomètre." Yet fascinating as he found his favourite science, he seems to have been haunted for some time before he quitted it with an uneasy feeling that there was a science yet nobler on which he ought to be employed. To divinity he had early determined himself, and one occurrence after another had diverted him from its special prosecution. During the last years of his professional life, this uneasiness appears to have increased upon him. Barrow's was not an unusual situation. He felt that he was held fast in the bond of a science which had early caught and enchained him; and yet he knew that he was not where he ought to be, till once he had given himself wholly to another which had still earlier and holier claims upon him. His first attempt was a compromise. He sought to impart a theological complexion to his mathematics. If he could not give himself to Bible divinity, he would at least study a divine philosophy. But he found that even this would not satisfy the claims of conscience. At his ordination he had vowed to serve God in the Gospel of his Son, and he could not make a Bible out of Euclid, nor a pulpit out of his mathematical chair. His only redress was to quit them both. The full extent of the feelings at work in the mind of this conscientious man, we have not the means of determining. May we hope that God, by his Spirit, was teaching him to "count all things but loss for the excellency of the knowledge of Christ Jesus his Lord?" Or was it only that he felt unhappy till he was engaged in the work which he had selected for the business of his life? Whatever was the reason, his abdication of the professorship confirms the remark, that "his whole history is one of resignation of profits upon principle." * Pemberton's "View of Sir Isaac Newton's Philosophy."-Preface. Pemberton's own opinion of Barrow is, that "he may be esteemed as having shewn a compass of invention equal, if not superior to any of the moderns, Newton only excepted." "Isaac Barrow, Theologian obscur, mathematicien plus connu." Encyclopedie Methodique. Montucla Histoire des Mathematiques, An. VII. tom. ii. p. 88. After this he lived quietly a fellow of his College, busied only in writing Sermons, many of which were never preached. The only preferment in the Churchwhich he obtained, was first a small sinecure in Wales from his uncle the Bishop of St. Asaph; and afterwards a prebendal stall in the Cathedral of Salisbury, from his friend Dr. Seth Ward, its Bishop. This preferment brought no increase of fortune to the contented holder; for he dispensed all the income in charity, and resigned both the one and the other as soon as he reached the summit of his earthly ambition in being made Master of Trinity College. That appointment took place in 1672. His predecessor was Dr. Pearson, whose ablest work is, like Barrow's own, an Exposition of the Creed. We suppose that the world is indebted for both works-one of them the most learned, and the other the most eloquent Exposition of the Apostles' Creed in the English language-to that statute of Trinity alluded to in Barrow's letter formerly quoted. Dr. Pearson was promoted to the Bishopric of Chester, and Barrow to the Mastership of Trinity. On that occasion the King made some small amends for the neglect with which he had, throughout. twelve years, treated the loyal son of a devoted servant. His Majesty had surely been long in discovering his most learned subject, and must have thought learning easily rewarded, when he had no bishopric to bestow on him, who, he said, "was the best scholar in England." As Andrew Melville said of the Kirk, he could say of his College-that he was wedded, and exceedingly indulgent to it. That wealthy corporation had been accustomed to uphold its credit for opulence by the style in which it maintained its Master. He was allowed the luxury of a coach, and had a variety of perquisites from the College revenue. All these Dr. Barrow remitted, and adopted wiser expedients for sustaining the magnificence of the foundation. He set on foot a subscription for building a College library, and made prodigious exertions in furthering his cherished project. Besides his own pecuniary contributions, which were large, he wrote letters to rich and influential personages, chiefly those who had been alumni of that College; and not content with soliciting their support, he always made a point of acknowledging any countenance which they might have given. The result of his zeal and unremitting labours, was the erection of an edifice which has ever since been one of the architectural glories of Cambridge, and which has from time to time received, in addition to its other acquisitions, the entire libraries of learned collectors. The only incident of a public kind which broke in upon the active retirement of his College life, was his election to the Vice-Chancellorship of the University-the duties of which did not prove onerous, and as soon as they were discharged, he gladly relinquished an office which he coveted the less because it was counted an honour. The Treatise on the Pope's Supremacy he did not live to publish. The state of his manuscript, preserved in Trinity College Library, indicates the prodigious pains which he had bestowed upon it, chiefly in the compilation of authorities. As it is, no one can open it at any page without being struck by its amazing research. Yet Barrow was not satisfied with what he had already quoted. Many confirmatory passages were still in his mind, for the insertion of which he had left blank spaces at the time. When on his death-bed, he placed the whole in the hands of Dr. Tillotson, saying, "I hope it is indifferent perfect, though not altogether as I intended it, if God had granted me longer life." Had he himself not indicated those omissions, no one could have detected them. "No argument of moment, nay hardly any consideration properly belonging to it, hath escaped his large and comprehensive mind. He hath said enough to silence the controversy for ever, and to deter all wise men, of both sides, from meddling any farther with it."* What the Archbishop has said about its arguments is equally true of its testimonies. In the words of a modern critic,-" We can imagine nothing whereunto to liken the glorious work of Barrow, but the mighty telescope of Herschel-an instrument which brings up, from the abyss of space, a countless multitude of luminaries, which hid themselves from the search of unassisted vision. Even so does the gigantic labour of Barrow call up from the depths of antiquity a galaxy of witnesses, who pass over our field of view in perfect order and distinctness, and shed a broad and steady illumination over the path of the inquirer." He was in the prime of life, and "occupying" amidst these labours, when the messenger of death came for him. He had gone to London in 1677, and on April 13, preached the Passion Sermon at Guildhall. This was the second sermon for which he ever received a pecuniary recompense, and was the last sermon, save one, which he ever spoke in public. It is a long discourse, and in some respects the most remarkable and intersting in his collected works. The exertion of delivering this sermon brought on a cold, which terminated in fever. The following account of his last sickness is from the pen of his affectionate friend Dr. Pope:-" The last time he was in London, whither he came, as it is customary, to the election of Westminster scholars, he went to Knightsbridge to give the Bishop of Salisbury a visit, and then made me engage my word to come to him at Trinity College immediately after the Michaelmas ensuing. I cannot express the rapture of joy I was in, having, as I thought, so near a prospect of his charming and instructive conversation, I fancied it would be a heaven on earth; for he was immensely rich in learning, and very liberal and communicative of it, delighting in nothing more than to impart to others, if they desired it, whatever he had attained by much time and study: but of a sudden all my hopes vanished, and were melted like snow before the sun.” The following particulars are recorded in the life of his successor, Dr. John North; though there seems to be a discrepancy regarding the place of his death:-"The good Dr. Barrow ended his days in London, in a prebend's house, that had a little stair to it out of the cloisters, which made him call it a man's nest, and I presume it is so called at this day. The Master's disease was a high fever. It had been his custom, contracted * Archbishop Tillotson, in his Preface. † British Critic, vol. ii. p. 149. when he was at Constantinople, in all his maladies, to cure himself with opium. And being very ill, probably augmented his dose, and so inflamed his fever, and at the same time obstructed the crisis; for he was as a man knocked down, and had the eyes of one distracted. Doctor North seeing him so, was struck with horror; for he, that knew him so well in his best health, could best distinguish; and when he left him, he concluded he should see him no more; and so it proved." Dr. Barrow was buried in Westminster Abbey. His friends, by a subscription among themselves, erected a marble monument, surmounted by a bust, to his memory. The inscription on that monument was composed by Dr. Mapletoft, Professor of Physic in Gresham College, who, like Barrow himself, afterwards relinquished medicine for the ministry. 66 ISAACUS BARROW. S. T. P. Regi Carolo 11. a Sacris. Vir prope divinus, et vere magnus, si quid magni habent Abi, Lector, et æmulare. Obiit rv. die Maii, Ann. Dom. MDCLXXVII. Monumentum hoc Amici posuere. What-like a man was Isaac Barrow?"-That question could have been more easily answered, were we in possession of an authentic portrait. The ensuing anecdote develops Barrow's preference of wisdom to money.Of his general habits not much now can be told. He was a very early riser, and with two exceptions, the immoderate use of fruit and tobacco, he was very temperate in his habits. "We were once going from Salisbury to London, he, Barrow in the coach with the Bishop, and I on horseback. As he was entering the coach, I perceived his pockets strutting out near half a foot, and I said to him,“What have you got in your pockets?" He replied, "Sermons." "Sermons!" said I, "give them to me, my boy shall carry them in his portmanteau, and ease you of that luggage." "But," said he, "suppose your boy should be robbed ?" "That is pleasant," I said; "do you think that there are persons padding on the road for sermons?" "Why, what have you?" said he. "It may be five or six guineas," I answered. Barrow replied, "I hold my sermons at a greater rate, for they cost me much pains and time." Well then," said I, "if you will secure my five or six guineas |