# Maclaurin, Colin (DNB00)

**MACLAURIN**, COLIN (1698–1746), mathematician and natural philosopher, was born at Kilmodan, N.B., in February 1698. His grandfather, Daniel Maclaurin, removed from an ancestral estate on the island of Tirrie, off Argyleshire, to Inverara, and helped to restore that town after the ruin of the civil wars; he was the author of some memoirs of his own times. His son John was minister of Glendaruel and afterwards of Kilmodan, and the author of an Irish version of the Psalms; by his marriage with a lady named Cameron he had three sons: John, who is noticed separately, Daniel, who died young, and Colin. He died six weeks after Colin's birth, and his wife died in 1707, having in the interval removed to Dumbarton for the sake of her children's education. Colin Maclaurin was thus, in his tenth year, left entirely to the care of his uncle, Daniel Maclaurin, minister of Kilfinan, Argyllshire, who sent him in 1709 to the university of Glasgow. His mathematical genius soon showed itself; many of the propositions which afterwards appeared in his 'Geometria Organica' were invented by him during his five years' course at the university. In his fifteenth year he took the degree of M.A, and wrote for this occasion a thesis ' On the Power of Gravity.' After a year spent in the study of divinity he quitted the university and went to live with his uncle.

In September 1717 he obtained the professorship of mathematics in the Marischal College of Aberdeen. The examiners reported that both 'M'Laurine' and his rival Walter Bowman 'were capable to teach Mathematicks anywhere.' In Euclid Mr. Bowman was much readier and distincter, but 'in the last tryall, M'Laurine plainly appeared better acquainted with the speculative and higher pairts of the Mathematicks' (*Fasti Acad. Mariscallana,* ed. P. J. Anderson, i. 147). In the vacations of 1719 and 1721 he visited London; on his first visit he made the acquaintance of Sir Isaac Newton and was admitted a member of the Royal Society; on his second visit he formed an intimate friendship with its president, Martin Folkes [q. v.] In 1722 Lord Polwarth, plenipotentiary of Great Britain at the congress of Cambray, engaged Maclaurin as travelling tutor to his eldest son. They spent some time together in Lorraine, where Maclaurin wrote a memoir on the percussion of bodies, which gained him in 1724 the prize of the Royal Academy of Sciences, and the substance of which was afterwards embodied in his treatise on fluxions. At Montpellier his pupil died, and Maclaurin returned to his professorial duties at Aberdeen. On 27 April 1725 he appeared before the council and expressed his regret for the long absence without leave with which they reproached him; he was 'reponed' for the time, but in the following anuary his office was declared vacant, and in February he sent in his demission (*ib*. p. 148). He had in fact during the previous November removed to the university of Edinburgh as deputy professor to James Gregory (1753–1821) [q. v.], whom age and infirmity had rendered incapable of teaching. For this appointment he was largely indebted to the influence of Newton, who wrote strongly recommending him to the patrons of the university, and promising to contribute 20*l*. a year towards the stipend if Maclaurin were appointed.

Maclaurin's classes at Edinburgh were numerously attended. During the session 1 Nov. to 1 June he spent four or five hours every day in teaching. He became a man of wide influence and many friends; and he used to the fullest extent the opportunities of usefulness opened to him. His skill in experimental physics, in astronomical observations, and in practical mechanics was constantly placed at the service both of public bodies and private individuals. He made the actuarial calculations for an insurance fund established by law for the widows and children of the Scottish clergy and professors in the universities. He extended the medical society of Edinburgh so as to include physics and antiquities, and became secretary of the new society, with Dr. Plummer as his colleague, the Earl of Morton being the first president. He proposed an astronomical observatory for Scotland, improved the maps of Orkney and Shetland, and was a firm believer in the existence of a north-polar passage.

In 1745 it was Maclaurin who organised the defences of Edinburgh against the rebel troops; he was employed night and day in planning the hastily raised fortifications and superintending their erection. His exertions
shattered his health; when the rebels obtained possession of Edinburgh he withdrew to England and became the guest of Thomas Herring [q. v.], then archbishop of York. Exposure to severe cold on his return home brought on dropsy of the belly, and he died on 14 June 1746 at the age of forty-eight. Within a few hours of his death he was engaged in dictating to an amanuensis a chapter 'Of the Supreme Author and Governor of the Universe, the true and living God,' which was the last chapter of his 'Account of the Philosophical Discoveries of Sir Isaac Newton.' The argument in favour of a future life contained in the last sentences of this unfinished chapter is now well known (see Martineau, *Study of Religion,* ii. 372); it proceeded from the lips of a dying man.

In 1733 he married Anne, daughter of Walter Stewart, solicitor-general for Scotland. Of his seven children two sons, John and Colin, and three daughters survived him. His eldest son, John Maclaurin, afterwards Lord Dreghorn, is separately noticed.

Gifted with a genius for geometrical investigation second only to Newton's, Maclaurin had no need to abandon Newton's methods in favour of any easier; and it was naturally more gratifying to his patriotism to develope the fluxional calculus to its fullest extent than to resort to the differential methods in use on the continent. The result was that Maclaurin, the one mathematician of the first rank trained in Great Britain in the last century, confirmed Newton's exclusive influence over British mathematics; and for three generations it was left to continental mathematicians to develope the modern methods of mathematical analysis.

Maclaurin's writings are: 1. 'Geometria Qrganica, sive Descriptio Linearum Curvarum Universalis ' (1720). This work was dedicated to Newton and received his *imprimatur* as president of the Royal Society, dated 12 Nov. 1719. Newton had discovered the theorem that if two angles of given magnitude be movable round their vertices, and the intersection of a side of the one with a side of the other be made to travel along a straight line, the intersection of the other pair of sides will describe a conic. Maclaurin developes this into a general method of reducing the description of a curve to the description of another curve of lower order; the theory is one of much beauty and power, and a remarkable production for so young a mathematician. A supplement, written in France in 1721, appeared in the 'Phil. Trans.' in 1735 (p. 439); it contains the general theorem, from which Pascal's follows as a corollary, that if a polygon be deformed so that all its sides passing respectively through fixed points, all its vertices except the last describe given curves of orders *m, n, p,* . . ., the last will describe a curve of order 2 *m n p* . . ., which will be lowered by *m n p* . . . when the fixed points lie on a straight line. These geometrical researches of Maclaurin were afterwards the starting point of further developments by Poncelet and others. 2. 'A Treatise of Fluxions,' 2 vols. Edinburgh, 1742. This work Lagrange described as 'le chef d'œuvre de geometric qu'on peut comparer a tout ce qu'Archimede nous a laissé de plus beau et de plus ingénieux' (*Mém. de l'Acad. de Berlin*, 1773). The book was translated into French by Pere Pezenas in 1749; the second English edition appeared in 1801, with a portrait of the author. This work grew out of his attempt to vindicate the fluxional calculus against the attacks of Bishop Berkeley (*Analyst*, 1734). The fundamental principles, many of which had been given in the 'Principia' with little or no proof, are here elaborately set out and based on the Euclidian geometry and many new and important applications to geometrical and physical problems are given. In particular his geometrical discussion of the attraction of an ellipsoid on an internal point, given in the second volume, so favourably impressed Clairaut that he abandoned the analytical method in its favour, in treating of the figure of the earth. His memoir on the gravitational theory of tides, which gained: one of the prizes of the French Academy of Sciences in 1740 and was written in haste for that purpose, is incorporated in a revised form in the second volume of his 'Fluxions.' His other two principal works appeared posthumously in 1748, his literary executors being Martin Folkes, Andrew Mitchell (M.P. for Aberdeen), and John Hill (chaplain to Archbishop Herring). They are 3. 'A Treatise of Algebra, with an Appendix De Linearum Geometricarum Proprietatibus Generalibus.' In the fifth edition (1788) this appendix is translated into English. A French translation of the algebra by Lecozic appeared at Paris in 1753, and a French translation of the appendix forms part of the 'Melanges de Geometric Pure' of F. de Jouquières. The algebra is an elementary treatise, dealing principally with equations, and with the application of algebra to geometry; it is a model of clear and terse exposition, and was in vogue as a Cambridge text-book for more than half a century (Wordsworth, *University Studies*). 4. 'An Account of Sir Isaac Newton's Philosophy,' published by subscription by Patrick Murdoch for the benefit of Maclaurin's children, and prefaced by a memoir of the author. The first draft of this work had been prepared for publication soon after Newton's death in 1728, by way of supplement to an account of Newton's life which was to have been prepared by his nephew, Conduitt; but the nephew's death prevented the execution of this plan. Besides the above works, he published in 1745 a revised and augmented edition of David Gregory's 'Practical Geometry,' which he translated into English. He had also in contemplation at the time of his death a complete course of practical mathematics.

The following papers by him appeared in the 'Philosophical Transactions of the Royal Society:' 1. 'Of the Construction and Measure of Curves,' No. 366. 2. 'A New Method of Describing all kinds of Curves,' No. 859. 3. 'A Letter to M. Folkes on Equations with impossible Roots' (May 1726), No. 894. 4. A second letter on the same subject (March 1729), No. 408. 5. 'On the Description of Curves, with an Account of further Improvements, and a Paper dated Nancy, 27 Nov. 1722,' No. 489. 6. 'An Account of the Treatise of Fluxions,' No. 467. 7. The same continued, No. 469. 8. 'A Rule for Finding the Meridional Parts of a Spheroid with the same Exactness as of a Sphere,' No. 461. 9. 'Of the Basis of the Cells wherein the Bees deposit their Honey,' No. 471.

[Works; an Account of the Author's Life and Works, prefixed to Maclaurin's Account of Newton's Philosophical Discoveries; Marie's Hist. des Sciences Math, et Phys. viii. 2–10; cf. also Montucla's Hist. des Math. iii. 86–7, iv. 184; W. W. R. Ball's A Short History of Mathematics, pp. 359–63.]