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Colin MacLaurin

MACLAURIN, COLIN, an eminent mathematician and philosopher, was descended from an ancient and respectable family, which had long been in possession of the island of Tiree, a solitary but comparatively fertile member of the Hebridean range. His grandfather, Daniel M’Laurin, removed thence to Inverary, and contributed greatly to restore that town, which was nearly ruined in the civil wars. He wrote some memoirs of his own times, and appears to have been a man of superior abilities. John, the son of Daniel, and father of Colin, was minister of the parish of Glenderule, where he was greatly beloved as a faithful and diligent pastor; he completed a version of the Psalms in Irish, which was generally used in those parts of the country where divine service was performed in that language. He married a lady of the name of Cameron, by whom he had three sons. John, the eldest, was for many years one of the ministers of the city of Glasgow, and well known as the author of several essays and sermons: he was also one of the most popular preachers of his day. Daniel, the second son, died at an early age, after having given proofs of surprising genius; and Colin, born at Kilmoddan, in the month of February, 1698. His father died six weeks after; but the loss to the family was not so severely felt as it otherwise might have been, on account of the kind advice and benevolent attention of a worthy uncle, the reverend Daniel Maclaurin, minister of Kilfinnan, and the careful economy and exemplary virtues of their mother. After remaining in Argyleshire for some time, on a small patrimonial estate, which was divided between Mrs Maclaurin and her sisters, she removed to Dumbarton, for the more convenient education of her children; but dying in 1707, the entire charge of the orphans devolved upon their uncle. Colin, at this time, was nine years old; and, although of a delicate constitution, he was remarkable for the quickness of his apprehension, and the retentiveness of his memory; he was passionately fond of learning, and pursued his studies with so much zeal and satisfaction, as to be fully qualified to enter the university of Glasgow, in two years after his mother’s death. He was accordingly placed there under the direction of Mr Carmichael, an admirable public teacher, who took the greatest pains in superintending his education, and for whom Mr Maclaurin, ever after in life, evinced the warmest feelings of gratitude and respect. His proficiency in every branch of elementary learning was so rapid, and his application to study so intense, that his teachers were astonished at the ease and quickness with which he distanced, not only those who were commencing the same class with himself, but those who had the advantage of attending for many sessions before him. His youthful imagination entered with great delight into the beauties of the writings of the ancients, and a taste for classical learning never forsook him during the whole course of his life, notwithstanding the predominant bent of his wonderful genius for the cultivation and improvement of mathematical science. From the time he entered college, he kept a diary, in which he carefully noted down the beginning and success of every particular study, inquiry, or investigation, his conversations with learned men, the subjects of those, and the arguments on either side. This was found among his oldest manuscripts, and in it might be read the names of the celebrated Mr Robert Simpson, Dr Johnson, and several other gentlemen of learning and worth, who all seemed anxious who should most encourage our young philosopher, by opening to him their libraries, and admitting him into their most intimate society and friendship. His genius for mathematical learning discovered itself so early as twelve years of age, when, having accidentally met with a copy of Euclid, in a friend’s chamber, he became master, in a few days, of the first six books, without any assistance; and having accomplished this extraordinary enterprise, his predilection for the science of quantity was determined for life. He now made an extraordinary progress, as we very soon after find him engaged in solving the most curious and difficult problems.

At fifteen years of age, Mr Maclaurin took his degree of master of arts, having passed through the curriculum, or public course of lectures appointed by the university, which must be attended before this honour can be gained. The subject he selected for his thesis, was, the "Power of Gravity," and this, according to the custom of the times, it was necessary for him to defend publicly. It may be necessary to observe, for the information of those who are acquainted with the manner in which such disputatious were conducted in Scotland, that the candidate was left free to select for this ordeal any literary or scientific subject he thought proper. The depth and boldness of the topic proposed by young Maclaurin at once revealed what kind of studies had engaged his attention while at the university, and excited the wonder and admiration of all present. In most instances, the subjects of disputation were of a trifling kind, and adapted chiefly to afford the candidate an opportunity of displaying his ingenuity and acquaintance with the mood and figure of the school of logic. But the mind of our youthful philosopher disdained to stoop to any thing puerile or common-place, and the sublimity of his subject showed at once the nature of his studies and the depth of his erudition. At that time the philosophy of Newton was comparatively unknown, and even men the most distinguished in science were slow to comprehend the great and important truths it contained. None but those profoundly skilled in geometry could fully comprehend his doctrines, and that of itself excluded many from the study; whilst others were bound in the trammels of the scholastic jargon of Aristotle, or the imaginary vortices of Des Cartes. When, therefore, young Maclaurin chose the "Power of Gravity" as the subject of his thesis, it was a presupposition that he was fully acquainted with the fundamental doctrines of Newton’s discoveries, and upon this occasion he acquitted himself to the wonder and delight of his auditors. He afterwards illustrated the same subject in a most beautiful manner, in the last two books of his account of the philosophical discoveries of Sir Isaac. There is only one instance more, in the whole range of literature, that we are acquainted with, of such extraordinary and precocious talent where a predisposition for mathematical science was any thing like so strong, and that is in the person of Pascal, whom Bayle calls the divine—nearly at the same age, though not exceeding that of our youthful philosopher. He, too, by the force of his irresistible genius, in secret and by stealth, may be said to have invented a system of geometrical science, which, to keep him in ignorance of, his father had sacrificed both fame and fortune. It might be invidious to compare the philosophic acquirements of these great men in after life, further than their mutual fondness for classic literature, in which they both proved themselves elegant writers. They had both a strong sense of religion on their minds, and to those who have perused their works, their most anxious desire must appear to have been to apply the theoretical propositions which were known, or they themselves had demonstrated, so as to promote the real benefit of mankind.

Maclaurin having made such an extraordinary progress in the study of geometry, and having, with little trouble, conquered difficulties which, in general, are looked upon as so formidable, passed at once to the higher branches of that science, and, instead of being deterred from exertion by the intricacy of the demonstrations which necessarily met him at every step as he proceeded in the investigation of difficult propositions, his energies seemed to acquire new life and vigour to enable him to surmount every obstacle in his way. Nothing delighted him more than to be engaged in difficult and curious problems, and this much is certain, that in his sixteenth year he had already invented many of the finest propositions afterwards published under the title of Geometria Organica.

At the beginning of the session in 1714, immediately subsequent to taking his degree, he entered himself as a student of divinity, but he only attended the college for one year longer, when, becoming disgusted at the dissensions that at that time had crept into the church, he relinquished all ideas of becoming a clergyman, and, happily for science, determined to devote himself to the study of mathematics and philosophy. He quitted the university and retired to his uncle’s house, at Kilfinnan, in a sequestered part of the country. That good man having, at all times, acted as a father to him, he determined to wait with patience until some secular employment should occur. In this happy seclusion, he continued his favourite researches, still cultivating his mind by a perusal of the best classic authors, for which he had naturally the most refined taste. The sublime scenery amidst which he lived, would, at proper intervals, invite him to wander through the lofty mountains and lonely glens, to consider the numberless natural curiosities with which they abound; and here his fancy being warmed by the grand scenes which presented themselves, he would sometimes break out in an ode, or hymn, on the beauties of nature, and the perfection of its Author. Of these, some fragments were preserved by his friends, and although we know not if they were ever published, still they must have possessed considerable interest, as serving to develop the openings and improvements of a mind like that of Maclaurin.

When Mr Maclaurin was only nineteen years old, in the autumn of 1717, a vacancy occurred in the professorship of mathematics in the Marischal college of Aberdeen. For this he presented himself as a candidate, and carried along with him the most ample testimonials from his friends at Glasgow, where he had distinguished himself so eminently. A very able competitor appeared in the field against him, but after a competition, or comparative trial of excellence, which lasted for ten days, Mr Maclaurin was declared the successful candidate. Being now fixed in his chair, he quickly revived the taste for mathematical learning, and raised it higher than it had ever been in that university. He continued at Aberdeen discharging the duties of his office, and had the happiness to perceive his usefulness increasing, and his popularity as a public professor greatly extended. In the vacations of 1717 and 1719, he went to London, with the view of extending his information, and of being introduced to the illustrious men there. As mathematical knowledge was never in so great request, nor its professors so much honoured at any period in the history of Britain, his fame had already gone before him; but, independent of that, he was furnished with letters of introduction from professor Simpson and Dr Clark, to the first philosophers of that or any other age. It was this first journey to London that laid the foundation of his subsequent fortunes in life. Besides Dr Hoadly, then bishop of Bangor, Dr Samuel Clark, and several other eminent men, he became acquainted with Sir Isaac Newton, who not only patronized him as a young man of genius, and possessed of a singular turn of mind for mathematical investigation, but seems to have formed for him a stronger degree of attachment than he was ever known to exhibit towards any one of the numerous candidates for his patronage. This kind preference, Mr Maclaurin ever after considered the greatest honour and happiness of his life. Long before he meditated his journey to London, he was an enthusiastic admirer of the philosophy of Newton, and of the almost superhuman genius of its inventor. To him he therefore submitted his treatise on the "Power of Gravity," which he brought with him, in manuscript, to London, and, on its receiving the sanction of him who had done more to extend the boundaries of mathematical science than almost all mankind, Mr Maclaurin’s triumph was complete. He was admitted a member of the Royal Society when only twenty-one years of age, and two of his papers were, about the same time, inserted in the transactions of that learned body, and his book, entitled Geometria Organica, was published with the approbation of their president. In his second journey, he became acquainted with Martin Folks, Esq., who succeeded Sir Isaac Newton as president of the Royal Society, and with whom he thenceforth cultivated a most entire and unreserved friendship. This great patron of scientific men frequently corresponded with him, communicating to him all his views and improvements in the sciences, and encouraging him to proceed in his philosophical studies.

In 1722, lord Polwarth, ambassador from the court of St James’s to the congress of Cambray, had been for some time looking out for a proper person to accompany his son, Mr Hume, on his travels. His lordship was fond of literature and the company of literary men; he had frequent opportunities of observing Mr Maclaurin’s behaviour, who at this time, from his consummate abilities, was admitted into the highest circles of society in London. His lordship being deeply prepossessed in favour of our youthful philosopher, engaged him as companion and tutor to his son. Maclaurin having procured a proper person to fill his place for a time at the college of Aberdeen, and feeling a strong desire to gratify his curiosity by visiting foreign countries, he accordingly with his friend and scholar set out for France, and proceeded at once to the capital, where they took up their abode. After remaining a short time at Paris, they visited several of the chief towns in France, and finally fixed upon Lorraine for their residence. Here they had the advantage of a good academy, besides the introduction to one of the most polite courts in Europe. Mr Maclaurin had now an opportunity of improving that easy and genteel address which was at all times natural to him, and with his graceful person and great erudition, he excited the admiration, and gained the esteem of the most distinguished persons of both sexes. Here he wrote his essay on the percussion of bodies, which gained the prize of the Royal Academy of Sciences in 1724. The substance of this tract is inserted in his Treatise of Fluxions.

On leaving Lorraine with his pupil on a tour through the southern provinces of France, and arriving at Montpelier, Mr Hume was seized with a fever which quickly terminated his life. This dreadful calamity affected Mr Maclaurin in the deepest manner and overwhelmed him with grief. In some letters written on that melancholy occasion, he seemed almost inconsolable for the loss of his pupil, companion, and friend, and his sympathy with a family to which he owed great obligations, and which had suffered an irreparable loss in the death of this hopeful young nobleman, rendered him unhappy beyond expression. Travelling and all other things being now distasteful, he set out immediately on his return to his profession at Aberdeen.

Having by this time justly earned the distinction of one of the first men of his country, the curators of the university of Edinburgh were desirous of engaging him to supply the place of Mr James Gregory, whose age and infirmities had rendered him incapable of teaching; but several difficulties retarded the design for some time. A gentleman eminent for mathematical abilities, but whose name is now forgotten, had succeeded in gaining over some of the patrons, who promised him their interest for the appointment, until a recommendatory letter from Sir Isaac Newton completely turned the balance in Mr Maclaurin’s favour. Sir Isaac first addressed Mr Maclaurin, with allowance to show it to the patrons of the university, and expresses himself as follows:—"I am very glad to hear that you have a prospect of being joined to Mr James Gregory in the professorship of mathematics at Edinburgh, not only because you are my friend, but principally because of your abilities, you being acquainted as well with the new improvements of mathematics as with the former state of those sciences; I heartily wish you good success, and shall be very glad of hearing of your being elected; I am, with all sincerity, your faithful friend, and most humble servant." In a second letter to the lord provost of Edinburgh, which Mr Maclaurin knew nothing of till some years after Sir Isaac’s death, he thus writes: "I am glad to understand that Mr Maclaurin is in good repute amongst you for his skill in mathematics, for I think he deserves it very well, and to satisfy you that I do not flatter him, and also to encourage him to accept the place of assisting Mr Gregory, in order to succeed him, I am ready (if you please to give me leave,) to contribute twenty pounds per annum towards a provision for him till Mr Gregory’s place becomes void, if I live so long, and, I will pay it to his order in London." The town council, however, with becoming pride, respectfully declined this generous offer, and the business was finally arranged that Mr Gregory was to retain his salary during life; his family in case of their father’s death were secured in it for seven years from the date of Mr Maclaurin’s being inducted as joint professor, who was promised fifty pounds per annum, besides the fees he received from the students attending the class, upon condition of performing all the duties of the office. On the 3d November, 1725, he was introduced to the university, as was at the same time his learned colleague and intimate friend, Dr Alexander Monro, professor of anatomy. The subjects which Mr Maclaurin introduced into the different courses of lectures on mathematics were very miscellaneous, and the classes soon became unusually numerous, there being upwards of a hundred young gentlemen attending his lectures, who being of different standings and proficiency, he was obliged to divide them into four or five classes, in each of which he employed a full hour every day, from the 1st of November to the 1st of June. In the first or lowest class, (sometimes divided into two,) he taught the first six books of Euclid’s Elements, plain trigonometry, practical geometry, the elements of fortification, and an introduction to Algebra. The second class repeated the Algebra again from its principles, and advanced farther in it, then proceeded to the theory of mensuration of solids, spherical trigonometry, the doctrine of the Sphere, dialling, and other practical parts. After this he gave the doctrine of the conic sections, with the theory of gunnery, and concluded with the elements of astronomy and optics. In the third class he went on in astronomy and perspective, prelected on Sir Isaac Newton’s Principia, and explained the direct and inverse method of fluxions. At a separate hour he began a class of experimental philosophy about the middle of December, which continued thrice every week till the beginning of April, and at proper hours of the night described the constellations and showed the planets by telescopes of various kinds. All Mr Maclaurin’s lectures on these different subjects were given with such perspicuity of method and language, that his demonstrations seldom stood in need of being repeated. Such, however, was his anxiety for the improvement of his scholars, that if at any time he found they could not comprehend his meaning, or if upon examining them he found they could not readily demonstrate the propositions which he had proved, he was apt rather to suspect that his own expressions had been obscure than their want of genius or attention. He, therefore, would resume the demonstration in some other method, in order to try, if, by presenting it in a different light, he could give them a better view of it. Besides the labours of his public profession, he had frequently many other employments and avocations, if an uncommon experiment was said to have been made any where, the curious were desirous of having it repeated by Mr Maclaurin. On all momentous occasions he was the first to be applied to; and if an eclipse or comet was to be observed, his telescopes were always in readiness. Such was the elegance and amenity of his manners, that the ladies took the liveliest interest in his experiments and observations, and were delighted and surprised at finding how easily and familiarly he would resolve the questions they put to him; and to those gentlemen who had been his pupils his advice and assistance were never wanting; nor was admittance refused to any except in his teaching hours, which were devoted to that purpose alone. The ingenious of all ranks courted his acquaintance and friendship, and so anxious and pressing were they to enjoy the pleasure of his company and conversation after his usual avocations were over, that he was obliged to take from the ordinary hours of repose what he bestowed on his scholars and friends, and by persevering in deep and severe study, he exhausted his strength and greatly impaired his health. About this time, at the beginning of the year 1728, Sir Isaac Newton died, and his nephew, Mr Conduitt, proposed to publish an account of his life, for which purpose he applied to Mr Maclaurin for his assistance, who out of gratitude to his great benefactor readily undertook the task, and finished the history of the progress which philosophy had made before Sir Isaac’s time. When the first draught of that work was sent up to London it was shown to some eminent judges, and met with their highest approbation. Among the rest Dr Rundle, afterwards bishop of Derry, was so pleased with the design that he mentioned it as particularly worthy of the Queen’s notice, who, after attentively perusing it, was so highly gratified that she expressed a desire to see it published; but Mr Conduitt’s death having prevented the execution of his part of the proposed work, Mr Maclaurin’s manuscript was returned to him. To this he afterwards added the more recent proofs and examples given by himself and others on the subjects treated by Sir Isaac, and left it in the state in which it now appears. Mr Maclaurin continued to live single till the year 1733, when, having a mind equally formed for the social endearments of refined society as those of the profoundest philosophy, he married Anne, daughter of Mr Walter Stewart, solicitor-general for Scotland to George the first, by whom he had seven children.

Dr Buckley, bishop of Cloyne, having taken occasion, from some disputes that had arisen concerning the grounds of the fluxionary method, in a treatise, entitled the Analyst, published in 1734, to explode the method itself, and at the same time to charge mathematicians in general with infidelity in religion, Mr Maclaurin entered the lists of disputation with him, eager to defend his favourite study and repel an accusation in which he was most unjustly included. He commenced his reply to the bishop’s book; but as he entered more deeply into the subject, so many discoveries, so many new theories and problems occurred to him, that, instead of a vindicatory pamphlet, his work, when finished, presented a complete system of fluxions, with their application to the most considerable problems in geometry and natural philosophy. This work was published in Edinburgh in 1742, in two volumes quarto, in which we are at a loss what most to admire—his solid, unexceptionable demonstrations of the grounds of the method itself, or its application to such a variety of curious and useful problems. A society had for many years subsisted in Edinburgh, for the advancement of medical knowledge; Mr Maclaurin, on reviewing their plan of proceedings, and not thinking it sufficiently extensive, proposed to take in all parts of physics, together with the antiquities of the country. This was readily agreed to, and Mr Maclaurin’s influence engaged several noblemen and gentlemen of the first rank and character, to join themselves for that purpose to the members of the former society. The earl of Morton did them the honour to accept of the office of president. Dr Plummer, professor of chemistry, and Mr Maclaurin, were appointed secretaries; and several gentlemen of distinction, English and foreigners, desired to be admitted members. At the monthly meetings of the society, Mr Maclaurin generally read some treatise of his own, or communicated the contents of his letters from foreign parts; by which means the society were informed of every new discovery or improvement in the sciences. Several of the papers read before this society, are printed in the 5th and 6th volumes of the Medical Essays; some of them are also published in the Philosophical Transactions; and Mr Maclaurin had occasion to insert a great many more in his Treatise of Fluxions, and in his account of Sir Isaac Newton’s philosophy. He was the first who proposed the building of an astronomical observatory, and a convenient school for experiments, in the university of Edinburgh, of which he drew an elegant and well contrived plan; and, as the work was to be carried on by private subscription, he used all his influence to raise money for that purpose with so much success, that, had not the Rebellion intervened in Scotland, the work would have been speedily completed. The earl of Morton, on visiting his estates in Orkney and Shetland in 1739, wanted at the same time to settle the geography of these islands, which was very erroneously laid down on all our maps, to examine their natural history, to survey the coasts, and take the measure of a degree of the meridian,—and for this purpose he applied to Mr Maclaurin for his assistance; but his domestic affairs not permitting him to undertake the journey, he drew up a plan of what he thought necessary to be observed, furnished the proper instruments, and recommended Mr Short, the celebrated optician, as a fit operator for managing them. The accounts Mr Maclaurin afterwards received of this voyage, made him still more sensible of the erroneous geography we had of those parts, by which so many shipwrecks had been occasioned, and he therefore employed several of his scholars, who were then settled in the northern counties, to survey the coasts.

Mr Maclaurin had still more extensive views for the improvement of geography and navigation over all the surface of the globe. After carefully perusing all the accounts of voyages, both in the South and North Seas, he was of opinion that the sea was most probably to be found open from Greenland to the South Sea, by the North Pole; and, when schemes for finding out such a passage were submitted to parliament in 1744, he was consulted concerning them by several persons of high rank and influence; but before he could finish the memorials which he proposed to have sent, the premium was limited to the discovery of a north-west passage, and Mr Maclaurin used to regret that the word west was inserted, because he thought a passage, if at all to be found, must lie not far from the pole. Of this he appeared to be so deeply persuaded, that he has been heard to say, if his situation could admit of such adventures, he would gladly undertake the voyage, even at his own cost.

Such was the zeal this amiable and celebrated man evinced on every occasion for the public good: the last and most remarkable instance, is that which we shall now relate.

In 1745, when the Highland army had got between Edinburgh and the king’s troops, Mr Maclaurin was the first to rouse the friends of the existing government from the security in which they had hitherto continued; and though he was aware that the city was not long defensible, or able to resist even the undisciplined and ill-armed host that was advancing to attack it, yet as he foresaw how much might be gained by the insurgents’ possessing themselves of the capital, and the king’s forces, under Sir John Cope, being daily expected, he made plans of the walls, proposed the several trenches, barricades, batteries, and all such defences as he thought could be thrown up before the arrival of the enemy, earnestly hoping that the town might thus hold out till relieved. The whole burden, not only of contriving, but also of overseeing the execution of this hasty defence, fell to Mr Maclaurin’s share. He was indefatigable in his exertions, employed both night and day in drawing plans, and running from place to place; so that the anxiety, fatigue, and cold to which he was thus exposed, affecting a constitution naturally weak, laid the foundation of the disease of which he died. It is not properly connected with our subject to inquire how Mr Maclaurin’s plans were neglected or defeated, or by what means prince Charles got possession of Edinburgh; but, after defeating the king’s troops at Prestonpans, he found himself in such strength as to issue several very arbitrary orders, among which was one commanding all who had been volunteers in the defence of the city, before a stated time, to wait on his secretary, to subscribe a recantation of what they had done, and a promise of submission to the new government, under the pain of being deemed and treated as rebels. Mr Maclaurin had acted too conspicuous a part as a volunteer, to hope to escape their vengeance, if he once fell into their hands; he therefore privately withdrew into England, before the last day of receiving the submissions, but not before he contrived means to convey a good telescope into the castle, and to supply the garrison with provisions.

Dr Thomas Herring, then archbishop of York, hearing that Mr Maclaurin had taken refuge in the north of England, invited him in the most friendly manner to reside with him during his stay in that part of the country. Mr Maclaurin gladly accepted the invitation, and soon after expresses himself thus in a letter to a friend:--"Here," says he, "I live as happily as a man can do who is ignorant of the state of his family, and who sees the ruin of his country." His grace of York, of whose talents and goodness Mr Maclaurin ever retained the highest veneration, held a frequent correspondence with him; and when it was suspected that the rebels might again enter Edinburgh on their retreat from England, he invited his former guest, for ease and security, to his hospitable mansion. While at York, it was remarked that Mr Maclaurin appeared more than usually meagre and sickly; but he, at that time, feeling no apprehension of danger, did not consider it necessary to call in medical aid. Having fallen from his horse, however, on his journey southward, and, when the Pretender’s army entered England, having, on his return home, been exposed to excessive cold and tempestuous weather, he complained upon his arrival of being seriously indisposed. His disease was soon discovered to be a dropsy in the abdomen, to remove which a variety of medicines were prescribed by the most eminent physicians of the day, and three tappings were resorted to, with little or no effect. While suffering under this painful malady, his behaviour was such as became a philosopher and Christian; calm, cheerful, and resigned; retaining his senses and judgment in their full vigour, till within a few hours of his death. Then, for the first time, while engaged in dictating to his amanuensis the last part of the last chapter of his Account of Sir Isaac Newton’s Discoveries, in which he proves the goodness of God, his amanuensis perceived him to falter. Dr Monro came in shortly afterwards, and he conversed with him after his accustomed manner, and requested him to account for flashes of fire, as it were, darting from his eyes, though his sight was gradually decaying, so that he could scarcely distinguish one object from another. His hands and feet were already cold, and no pulse could be traced in any part of his body. In a short time he desired to be laid upon his bed, where he breathed his last, on the 14th June, 1746, aged forty-eight years and four months. His wife, two sons, and three daughters, survived him. John, the eldest son, studied the law, and after making a distinguished figure at the bar, was promoted to the bench, 17th January, 1789, under the designation of lord Dreghorn. He was an excellent scholar, and erected a monument to his father in the Grey Friars’ churchyard, with an inscription which has often been quoted for its simple and expressive eloquence. Lord Dreghorn also published various pieces in prose and verse, which, in their day, enjoyed some reputation, and have been oftener than once printed.

Colin Maclaurin was not only distinguished by his great genius and learning but by the qualities of his heart, his universal benevolence, and unaffected piety. Dr Monro, in an oration spoken at the first meeting of the university after his death (from which much of the foregoing account is taken,) draws a sublime and affecting picture of his friend’s great qualities, and professes that, after an intimacy with him for so many years, he had but half known his worth which only disclosed itself in its full lustre, when it came to suffer the severe test of that distressful situation in which every man must at last find himself, and which only minds prepared like his, armed with virtue, can bear with dignity.

If we look back upon the numerous writings of Mr Maclaurin, and the deep researches he had been engaged in, his patience and assiduity will be equally astonishing with his genius. His favourite studies were mathematics, which he cultivated with wonderful success, influenced by a disinterested love of truth, and aiming constantly at improvement and utility. The further he advanced in the knowledge of geometry and of nature, the greater his aversion grew to perfect systems, hypotheses, and dogmatizing. Without being dissatisfied with the attainments we can arrive at, or the uses which they serve, he saw that there lay infinitely more beyond our reach, and used to call our highest discoveries but a dawn of knowledge, suited to our circumstances and wants in life, in which, however, we ought thankfully to acquiesce for the present, in hopes that it will be improved in a happier and more perfect state. To a view of general utility, all his studies were accommodated; and we find in many places of his works, an application even of the most abstruse theories, to the perfecting of mechanical arts. He had resolved, for the same purpose, to compose a course of practical mathematics, and to rescue several branches of the science from the bad treatment which they often meet with in less skilful hands. But all those designs were frustrated by his death, unless we may reckon as a part of his intended work, the Translation of Dr David Gregory’s Practical Geometry, which he revised and published, with additions, in the year 1745. In his lifetime, however, he often had the pleasure to serve his friends and country, by his superior skill Whatever difficulty occurred concerning the construction or perfecting of machines, the working of mines, the improvement of manufactures, the conveying of water, or the execution of any public work, Mr Maclaurin was at hand to resolve it. He was likewise employed to terminate some disputes of consequence, that had arisen at Glasgow, concerning the gauging of vessels; and for that purpose presented to the commissioners of excise two memorials containing rules (by which the officers afterwards acted,) with their demonstrations. But what must have given his philanthropic mind a higher source of pleasure than any thing else of the kind, were the calculations he made relative to that wise and humane provision, which is established by law, for the children and widows of the Scottish clergy, and of the professors in the universities, entitling them to certain annuities and sums, upon the voluntary annual payment of a certain sum by the incumbent. On the contrivance and adjustment of this scheme, Mr Maclaurin bestowed great labour, and contributed not a little to bring it to perfection.

To find that his knowledge rendered him thus eminently useful to a late posterity, must have been a delightful enjoyment. But what still more endeared his studies to him, was the use they were of in demonstrating the being and attributes of the Almighty Creator, and establishing the principles of natural religion on a solid foundation, equally secure against the idle sophistry of Epicureans, and the dangerous refinements of modern metaphysicians.

To this use Mr Maclaurin frequently applied them; and he was equally zealous in the defence of revealed religion, which he would warmly undertake, whenever he found it attacked, either in conversation or writing. How firm his own persuasion of its truth was, appears from the support which it afforded him in his last hours.

Among Mr Maclaurin’s productions, besides the articles already specified, was a paper sent to the Royal Academy of Sciences, at Paris, in the year 1740, on account of which he shared the prize of the Academy with the celebrated D. Bernouilli and Euler, for resolving the problems relating to the motion of the tides, from the theory of gravity—a question which had been given out during the former year, without receiving any solution. Having only ten days in which to draw up this paper, he had not leisure to transcribe a fair copy of it; so that the Paris edition of it is incorrect. Afterwards, however, he revised the whole, and inserted it in his Treatise of Fluxions. His contributions to the Philosophical Transactions, may be seen in different volumes of these collections, from No. 30 to No. 42, both inclusive, and treat on the following subjects:--"Of the Construction and Measure of Curves,"—"A New Method of describing all kinds of Curves,"—"On Equations with impossible Roots,"—"On the Description of Curves, with an Account of further Improvements, &c."—"An Account of the Annular Eclipse of the Sun at Edinburgh, January 27, 1742-3,"—"A Rule for finding the Meridianal Parts of a Spheroid, with the same exactness as of a Sphere,"—And "Of the Bases of the Cells wherein the Bees deposite their Honey." These papers conclude the list of our author’s writings, which were published during his lifetime. After his death, the friends, to whose judgment he submitted the disposal of his MSS., gave directions for publishing his "Treatise of Algebra," and his "Account of Sir Isaac Newton’s Philosophical Discoveries." The first of these works, which appeared in 1748, though it had not the advantage to be finished by his own hands, is yet allowed to be excellent in its kind; containing, in one volume, octavo, of a moderate size, a complete elementary treatise of the science of algebra, as far as it had been hitherto carried. Subjoined to it, by way of appendix, is a Latin tract, "De Linearum Geometricarum proprietatibus generalibus," which appears to have been, in our author’s judgment, one of the best of his performances, and in which he employed some of the latest hours that he could give to such studies, revising it for the press, as his last legacy to the sciences and the public.

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