Page:Dictionary of National Biography volume 35.djvu/203

Maclaurin 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, 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 (, University Studies). 4. 'An Account of Sir Isaac Newton's Philosophy,' published by