MACLAURIN, COLIN, a very eminent mathematician and philosopher, was the son of a clergyman, and born at Kilmoddan, Argyleshire, 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 a 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 the country seat of an 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 Sir Isaac Newton and other eminent men, at which time also he was admitted a member of the Royal Society.
In 1722 Lord Polwarth, plenipotentiary of the King of Great Britain at the Congress of Cambray, 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 their residence 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 professorship 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. He had some difficulties to encounter; but at length these were all surmounted, principally through Sir Isaac Newton, and he was introduced into the university in November 1725.
In the year 1733 he married Anne, the daughter of Mr Walter Stewart, solicitor-general for Scotland. 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 became a complete system of fluxions, with their application to the most important
problems in geometry and natural philosophy. This work was published in Edinburgh in 1742, in 2 vols. quarto, and is the most considerable of all his works. In the meantime, he was continually bringing forward 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.
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 these islands, which was then very erroneous in all 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 not destined to succeed, viz., the opening of a passage from Greenland to the South Sea by the north 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 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. 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 improvement of manufactures, the conveying of water, or the execution of any other public work, he was at hand to resolve it.
Of his works, we have mentioned the 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. (See the Fourth and Fifth Dissertations prefixed to this work.)