162 M A C M A C In this he investigated the attraction of an ellipsoid of revolution, and showed that a homogeneous fluid mass revolving uniformly round an axis under the action of gravity ought to assume the form of an ellipsoid of revolu tion. The importance of this investigation in connexion with the theory of the tides, the figure of the earth, and other kindred questions has always caused it to be regarded as one of the great problems of mathematical physics. Thus Clairfmfc, D Alembert, Lagrange, Legendre, Laplace, Gauss, Ivory, Poisson, Jacobi, Chasles, and other eminent mathematicians have successively attacked the problem, and in doing so have declared their obligations to Maclaurin as the creator of the theory of the attraction of ellipsoids. Lagrange s statement as to Maclaurin s dis coveries deserves to be especially cited : after observing that the attraction of a spheroid of revolution is one of the problems in which the method of the ancients has advantages over that of modern analysis, he adds that Maclaurin s investigation is "un chef d reuvre de geometric qu on peut comparer a tout ce qu Archimede nous a Iaiss6 de plus beau et de plus inge"nieux " (Mem. de I Acad. de Berlin, 1773). It may be added that Maclaurin was the first to introduce into mechanics, in this discussion, the important conception of surfaces of level, namely, surfaces at each of whose points the total force acts in the normal direction. He also gave in his Fluxions, for the first time, the correct theory for distinguishing between maxima and minima in general, and pointed out the importance of the distinction in the theory of the multiple points of curves. In 1745, when the rebels, having got between Edinburgh and the king s troops, were marching on that city, Maclaurin took a most prominent part in preparing trenches and barricades for its defence. This occupied him night and day, and the anxiety, fatigue, and cold to which he was thus exposed, affecting a constitution naturally weak, laid the foundation of the disease to which he afterwards succumbed. As soon as the rebel army got possession of Edinburgh, Maclaurin fled to England, to avoid making the submission to the Pretender which was demanded of all who had defended the town. He accepted the invita tion of Dr Herring, then archbishop of York, with whom he remained until it was safe to return to Edinburgh. From that time his health was broken, and he died of dropsy on June 14, 1746, at Edinburgh, in his forty-eighth year. Maclaurin was married in 1733 to A.nne, daughter of Walter Stewart, solicitor-general for Scotland. His eldest son, John, born in 1734, was distinguished as an advocate, and appointed one of the judges of the Scottish Court of Session, with the title of Lord Dreghorn. He inherited an attachment to scientific discovery, and was one of the founders of the Royal Society of Edinburgh, in 1782. After Maclaurin s death his account of Newton s philosophical dis coveries was published, and also his algebra in 1748. As an appen dix to the latter appeared his work, DC linearum gcomctricarum pro- pricfatibus gcneralibus tradatus, a treatise of remarkable elegance. Of the more immediate successors of Newton in Great Britain Maclaurin is probably the only one who can be placed in competi tion with the great mathematicians of the Continent at the time, .and his name will ever be held in remembrance in connexion with his important discoveries. Among his publications in the Philo sophical Transactions the following should be noticed : (1) "Tractatus de curvarum constructione et mensura, ubi plurimre series curvarum infinitse vel rectis mensurantur, vi-1 ad simpliores curvas reducantur," May 1718. The series of curveshere treated are what are now styled "pedal" curves, which hold an important place in the modern discussion of curves. Maclauvin established many geometrical properties connecting a curve with its pedal. He inves tigated the properties of the successive pedals of a circle with respect to a point on its circumference, also those of the pedals of curves for which the perpendicular on the tangent varies as some power of the radius vector drawn to the point of contact. (2) " Nova methodus universalis curvas omnes cujuscunque ordinis mechanice dcscribendi sola datorum angulorum et reetarum ope," January 1719. This and March 1729. In these papers he gave a proof of Newton s rule for the discovery of the number of imaginary roots of an equation. He added some general results on the limits to the roots, and gave the well-known method of finding equal roots by aid of the first derived equation. (5) " Observation of the Eclipse of the Sun of February 18, 1737, January 1738. (6) " On the Bases of the Cells where Bees Deposit their Honey," November 1743. French, translations of his Treatise on Fluxions and that on Newton s philosophical discoveries were published at Paris in 1749. His algebra was also translated into French, in 1753. (B. W.) M LENNAN, JOHN FERGUSON, LL.D. (1827-1881), one of the most original of modern inquirers into the con stitution of early society, was born at Inverness 14th October 1827. He studied at King s College, Aberdeen, where he graduated with great distinction in 1849, and then proceeded to Cambridge, where he remained till 1855, but did not take his degree. After some years spent in literary work and legal studies in London and Edinburgh, he joined the Scottish bar (January 1857). In 1865 he published an epoch-making study on Primitive Marriage, in which, starting from the prevalence of the symbolical form of capture in marriage ceremonies, and combining with great argumentative power a variety of phenomena of primitive society previously quite obscure, he developed an intelligible picture of the growth of the marriage relation and of systems of kinship (see FAMILY) according to natural laws. Continuing his studies on allied topics, M Lennan published in 1866 (Fortnightly Review, April and May 1866) an essay on "Kinship in Ancient Greece," in which he proposed to test by early Greek facts the theory of the history of kinship set forth in Primitive Marriage, and, three years later, a series of essays on "Totemism" (Fortnightly Review, 1869-70) (the germ of which had been contained in the paper just named), which mark the second great step in the systematic study of early society, to which the energies of his life were now devoted. A reprint of Primitive Marriage, with " Kinship in Ancient Greece " and some other essays not previously published, appeared in 1876 under the title of Studies in Ancient History, The new essays contained in this volume were mostly critical, but one of them, in which perhaps his guessing talent is seen at its best, on "The Divisions of the Irish Family," is an elaborate discussion of a problem which has long puzzled both Celtic scholars and jurists; and in another, " On the Classificatory System of Relation ship," he propounded a new explanation of a series of facts which, he thought, might be made to throw a flood of light upon the early history of society, at the same time putting to the test of those facts the theories he had set forth in Primitive Marriage. Papers on " The Levirate and Poly andry," following up the line of his previous investigations, appeared in the following year (Fortnightly Review, 1877), and were the last work he was able to publish. From 1872 to 1875 his literary plans were much interrupted by his duties as parliamentary draftsman for Scotland, and when he retired from this office his health was broken; his last years were chiefly spent abroad, and in spite of the self-denying assistance of his second wife (his first wife, a daughter of M Culloch the political economist, died in 1870, and he married again in 1875) the vast materials which he had accumulated for a comprehensive work on his favourite subjects were left only partially worked up, though the publication of his remains may still be looked for. Ho died 14th June 1881. In private life M Lennan was distinguished by his remarkable powers of conversation, by an uncompromising sense of duty, especially of duty to
tru^h, by a warm and affectionate disposition, and by his