COLIN, a very eminent mathematician and philosopher, was the son of a clergyman, and born at Kilmoodan, Scotland, in 1698. In the year 1709 he was sent to the university of Glasgow, where he continued five years, and applied himself intensely to study. His great genius for mathematical learning discovered itself as early as the age of twelve, when, having accidentally met with an Euclid in a friend's chamber, he became in a few days master of the first six books without any assistance; and it is certain, that in his sixteenth year he had invented many of the propositions which were afterwards published under the title of Geometria Organica. In his fifteenth year he took the degree of master of arts, and on that occasion composed and publicly defended, with great applause, a thesis on the power of gravity. After this he quitted the university, and retired to a country-seat of his uncle, who had the care of his education; for his parents had been some time dead. Here he spent two or three years in pursuing his favourite studies; but, in 1717, he offered himself as a candidate for the professorship of mathematics in the Marischal College of Aberdeen, and obtained it after a ten days' trial with a very able competitor. In 1719 he went to London, where he became acquainted with Dr Hoadly, then bishop of Bangor, Dr Clarke, Sir Isaac Newton, and other eminent men, at which time also he was admitted a member of the Royal Society; and in another journey in 1721, he contracted an intimacy with Martin Folkes, the president of the society, which continued until his death.

In 1722, Lord Polwarth, plenipotentiary of the king of Great Britain at the congress of Cambrai, engaged him to become tutor and companion to his eldest son, who was then about to set out on his travels. After a short stay at Paris, and visiting other towns in France, they fixed in Lorraine, where Maclaurin wrote his tract on the percussion of bodies, which gained the prize of the Royal Academy of Sciences for the year 1724. But his pupil dying soon afterwards at Montpellier, he returned immediately to his profession at Aberdeen. He was hardly settled there, however, when he received an invitation to Edinburgh; the curators of that university being desirous that he should supply the place of Mr James Gregory, whose great age and infirmities had rendered him incapable of teaching. He had some difficulties to encounter, arising from competitors, who had good interest with the patrons of the university, and also from the want of an additional fund for the new professor; but at length these were all surmounted, principally by the means of Sir Isaac Newton. In November 1725 he was introduced into the university. After this, the mathematical classes soon became very numerous, there being generally upwards of a hundred young gentlemen attending his lectures every year, who being of different standing 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 first of November till the first of June.

He lived a bachelor till the year 1733; but being not less formed for society than for contemplation, he then married Anne, the daughter of Mr Walter Stewart, solicitor-general for Scotland. By this lady he had seven children, of whom two sons and three daughters, together with his wife, survived him. In 1734, Berkeley, bishop of Cloyne, published a piece called The Analyst, in which he took occasion, from some disputes which had arisen concerning the grounds of the method of fluxions, to attack the method itself, and also to charge mathematicians in general with infidelity in religion. Maclaurin thinking himself included in this charge, began an answer to Berkeley's book; but, as he proceeded, so many new theories and problems occurred to him, that instead of a vindicatory pamphlet, his work came out a complete system of Fluxions, with their application to the most considerable problems in geometry and natural philosophy.

This work was published at Edinburgh in 1742, in two vols. quarto; and as it cost him infinite pains, so it is the most considerable of all his works. In the mean time, he was continually obliging the public with some performance or observation of his own, many of which were published in the fifth and sixth volumes of the Medical Essays at Edinburgh. Some of them were likewise published in the Philosophical Transactions, particularly, 1. Of the Construction and Measure of Curves; 2. A new Method of describing all kinds of Curves; 3. A Letter to Martin Folkes, Esq. on Equations with impossible Roots, May 1726; 4. Continuation of the same, March 1729; 5. On the Description of Curves, with an account of farther improvements, and a paper dated at Nancy, November 27, 1722; 6. An account of the Treatise of Fluxions, January 27, 1742; 7. The same continued, 10th March 1742; 8. A Rule for finding the meridional parts of a Spheroid with the same exactness as of a Sphere, August 1741; 9. Of the basis of the cells wherein the Bees deposit their Honey, 3d November 1734.

In the midst of these studies, he was always ready to lend his assistance in contriving and promoting any scheme that might contribute to the service of his country. When the Earl of Morton set out in 1739 for Orkney and Zetland, to visit his estates there, he desired Mr Maclaurin to assist him in settling the geography of those countries, which is very erroneous in all our maps; to examine their natural history, survey the coasts, and measure a degree of the meridian. Maclaurin's family affairs, and other connections, would not permit him to do this; he, however, drew up a memorial of what he thought necessary to be observed, furnished the proper instruments, and recommended Mr Short the optician as a fit person for the management of them. He had still another scheme for the improvement of geography and navigation, of a more extensive nature; which was the opening of a passage from Greenland to the South Sea by the north pole. That such a passage might be found, he was so fully persuaded, that he has been heard to say, that if his situation admitted of such adventures, he would undertake the voyage, even at his own charge. But when schemes for discovering it were laid before the parliament in 1744, and he was himself consulted by several persons of high rank concerning them, before he could finish the memorials which he proposed to send, the premium was limited to the discovery of a north-west passage; and he used to regret that the word west was inserted, because he conceived that the passage, if it existed at all, would be found not far from the pole.

In 1745, having been very active in fortifying the city of Edinburgh against the Highland army, he was obliged to fly from thence to the north of England, where he was invited by Herring, then archbishop of York, to reside with him during his stay in this country. In this expedition, however, being exposed to cold and hardships, and naturally of a weak and delicate constitution, he laid the foundation of an illness which put an end to his life, in June 1746, at the age of forty-eight.

Mr Maclaurin was a good as well as a great man, and worthy of esteem as well as admiration. His peculiar merit as a philosopher consisted in this, that all his studies were accommodated to general utility; and we find, in many places of his works, an application even of the most abstruse theories, to the perfecting of the mechanical arts. For this purpose, he had resolved to compose a course of practical mathematics, and to rescue several useful branches of the science from the bad treatment which they had often met with in less skilful hands. But all this was prevented by his death; unless we should reckon, as part of his intend- ed work, the translation of Dr David Gregory's Practical Geometry, which he revised, and published with additions in 1745. In his lifetime, however, he had frequent opportunities of serving his friends and his country by his great skill. Whatever difficulty occurred concerning the constructing or perfecting of machines, the working of mines, the improving of manufactures, the conveying of water, or the execution of any other public work, he was at hand to resolve it. He was likewise employed to terminate some disputes of consequence which had arisen at Glasgow concerning the gauging of vessels; and for that purpose presented to the Commissioners of Excise two elaborate memorials, with demonstrations, containing rules by which the officers now act. He also made calculations relating to the provision, now established by law, for the widows and children of the Scotch 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 incumbents. In contriving and adjusting this wise and useful scheme he bestowed a great deal of labour, and contributed not a little towards bringing it to perfection. Of such a man, it may be said that he lived to some purpose; which can hardly be predicated of those, how uncommon soever their abilities and attainments, who spend their whole time in abstract speculations, and produce nothing really useful or serviceable to their fellow-creatures.

Of his works, we have mentioned his Geometria Organica, in which he treats of the description of curve lines by continued motion. We need not repeat what has been said concerning the paper which gained the prize of the Royal Academy of Sciences in 1724. In 1740 the academy adjudged him a prize, which did him still more honour, for solving the motion of the tides from the theory of gravity; a question which had been given out the previous year, but without receiving any solution. He had only ten days to draw up this paper, and could not find leisure to transcribe a fair copy; so that the Paris edition of it is incorrect. He afterwards revised the whole, and inserted it in his Treatise of Fluxions; as he did also the substance of the former paper. These, with the Treatise of Fluxions, and the pieces printed in the Philosophical Transactions, of which we have given a list, are all the writings which Maclaurin lived to publish. Since his death, two more volumes have appeared, containing his Algebra, and his Account of Sir Isaac Newton's Philosophical Discoveries. His Algebra, though not finished by himself, is yet allowed to be excellent of its kind, containing, in a volume of no great bulk, a complete elementary treatise of that science, as far as it had then been carried. The occasion of his Account of Sir Isaac Newton's Philosophy may be shortly stated. Sir Isaac having died in the beginning of 1728, his nephew, Mr Conduitt, proposed to publish an account of his life, and desired Mr Maclaurin's assistance. The latter, out of gratitude to his great benefactor, cheerfully undertook, and soon finished, the history of the progress which philosophy had made before Sir Isaac's time; and this was the first draught of the proposed work; but as the latter did not go forward, on account of Mr Conduitt's death, the manuscript was returned to Mr Maclaurin. To this he afterwards made great additions, and left it in the state in which it now appears. See the Dissertations prefixed to this work.