MACKENZIE, SIE GEORGE (1636–1691), of Rosehaugh, knight, a prominent Scottish lawyer, was the grandson of Kenneth, first Lord Mackenzie of Kintail, and the nephew of Colin and George, first and second earls of Seaforth; his mother was a daughter of Dr Andrew Bruce, principal of St Leonard's College, St Andrews. He was born at Dundee in 1636, and, having passed through the grammar school there, was sent at an early age to college at Aberdeen, and afterwards at St Andrews, graduating at sixteen. He then engaged for three years in the study of the civil law at Bourges; on his return to Scotland he was called to the bar in 1656, and before the Restoration had risen into considerable practice. Immediately after the Restoration he was appointed a "justice-depute," and it is recorded that he and his colleagues in that office were ordained by the parliament in 1661 "to repair, once in the week at least, to Musselburgh and Dalkeith, and to try and judge such persons as are there or thereabouts delate of witchcraft." In the same year he acted as counsel for the marquis of Argyll; soon afterwards he was knighted, and he represented the county of Ross during the four sessions of the parliament which was called in 1669. He succeeded Sir John Nisbet as king's advocate in August 1677, and in the discharge of this office became implicated in all the worst acts of the Scottish administration of Charles II., earning for himself an unenviable distinction as "the bloody Mackenzie." His refusal to concur in the measures for dispensing with the penal laws against Catholics led to his removal from office in 1686, but he was reinstated in February 1688. At the Revolution, being a member of convention, he was one of the minority of five in the division on the forfeiture of the crown. King William was urged to declare him incapacitated for holding any public office, but refused to accede to the proposal. When the death of Dundee (September 1689) had finally destroyed the hopes of his party in Scotland, Mackenzie betook himself to Oxford, where, admitted a student by a grace passed on June 2, 1690, he was allowed to spend the rest of his days in the enjoyment of the ample fortune he had acquired, and in the prosecution of his literary labours. One of his last acts before leaving Edinburgh had been to pronounce (March 15, 1689), as dean of the faculty of advocates, the inaugural oration at the foundation of the Advocates' Library. He died at Westminster on May 8, 1691, and was buried in Greyfriars churchyard, Edinburgh. While still a young man Sir George Mackenzie appears to have aspired to eminence in the domain of pure literature, his earliest publication having been Aretina, or a Serious Romance (anon., 1660); it was followed, also anonymously, by Religio Stoici, a Short Discourse upon several Divine and Moral Subjects (1663), A Moral Essay, preferring Solitude to Public Employment (1665), and one or two other disquisitions of a similar nature. None of these earlier efforts are now read, if they ever were; and perhaps Mackenzie's strongest claim to be remembered at all in connexion with belles lettres is that which rests upon Dryden's grateful reminiscence of some stimulating conversation held with that noble wit of Scotland, Sir George Mackenzie," about 1673. (See Dryden's "Discourse on the Origin and Progress of Satire," prefixed to his Juvenal in 1693.) His most important legal works are entitled A Discourse upon the Laws and Customs of Scotland in Matters Criminal (1678), Observations upon the Laws and Customs of Nations as to Precedency, with the Science of Heraldry (1680), Institutions of the Law of Scotland (1684), and Observations upon the Acts of Parliament (1686); of these the last-named is the most important, the Institutions being completely overshadowed by the similar work of his great contem porary Stair. In his Jus Regium: or the Just and Solid Foundalions of Monarchy in general, and more especially of the Monarchy of Scotland, maintained (1684), Mackenzie appears as an uncompromising advocate of the highest doctrines of prerogative. His Vindication of the Government of Scotland during the reign of Charles II. is valuable as a piece of contemporary history. The collected Works were published at Edinburgh (2 vols. fol.) in 1716-22; and Memoirs of the Affairs of Scotland from the Restoration of King Charles II., from previously unpublished MSS., in 1821. It may be well to add that the subject of this notice must not be confounded with Dr George Mackenzie, the author of Lives and Characters of the Most Eminent Writers of the Scots Nation (1708-22). MACKENZIE, HENRY (1745-1831), was born at Edinburgh in August 1745. His father was Dr Joshua or Josiah Mackenzie, a successful physician, who also cultivated letters in a small way. Mackenzie got the ordinary education of a youth in his position at the high school and university of Edinburgh, and was afterwards articled to Mr Inglis, who was then attorney for the crown in the management of exchequer affairs. To this comfortable post the author in due time succeeded, and perhaps knew as little as any of that tribe ever did about the struggles and sorrows of a literary career. For his work's sake it would have been better if he had travelled some of life's rougher paths, or else been content to write about what he had actually seen in the Scottish world of that day.. There was plenty of material there if he had had the open eye to see it, as Walter Scott showed by and by; and it is a pity that Mackenzie did not try his hand at it, having been more in the heart of it than Scott could ever have been. As it is, his stories are clearly not the fruit of his experience, but rather the echo of his reading. He could write graceful enough sentences, somewhat artificial, yet smooth and pointed; but the men he describes are mere shadows, and the life altogether unreal. His first and best-known work, The Man of Feeling, was published anonymously when he was only twenty-six years of age, and soon became highly popular. It was a droughty season in Scottish literature, and therefore any little blossom, however sickly, was welcome for its rarity. Hume and Robertson and Smith had left the scene; Burns was just learning to think of the daisy he turned up with his ploughshare, and Fergusson had lately closed his brief and troubled career. Mackenzie had the field all to himself, and got the attention which is given to a solitary figure. He had read the Sentimental Journey, as one can see from expressions here and there, as well as from the affectation of writing his story in a fragmentary form; but he had not a gleam of Sterne's humour to relieve the sentimentality. He had read Richardson too, but he had none of that writer's subtle insight into character. Perhaps Goldsmith was his real model, but the likeness was as that between a firefly and a star. The "man of feeling" is a weak foolish creature, possessed with a futile benevolence, who goes up to London, where his friends should never have let him go, and meets a variety of sharpers, and comes out of their hands pretty much as Goldsmith makes the vicar's son do, only without the fun that clings to poor Moses. For this book is all in one key, sentimental and lachrymose, and the hero dies at last, from no particular cause, in a highly tragic fashion beside his fainting mistress. His next work, The Man of the World, is the picture of a born villain, a rogue in grain, who begins his rascality at school, perhaps earlier, and carries it through with entire consistency to the end. The man is unnaturally bad, and the incidents only find a place in some third-rate penny paper, if even are badly unnatural; and such a book at present would there. Julia de Roubigné, his only other novelette, was meant to depict the misfortunes of a number of quite blameless people-to be, in short, a tragedy without a villain, an Othello without an Iago. But, as it has no insight, and does not even try to have any insight, into the mystery of such calamities, the result is insipid and tedious. All these works had great popularity in their day; but that day is long past, and what life they now have is only a tradition. Mackenzie also wrote several dramas, mostly of the tragic sort, for in that tone he had won his successes, such as they were. character, of human individuality, was not likely to succeed in the drama, which depends more on that than on anything; and hence it was not our author's good fortune to deliver his country from the stigma of never having produced a genuine tragedy. Of The Spanish Father, The Prince of Tunis, and The Shipwreck, the second was brought on the stage, and managed to live for six nights; the other two were stillborn, and probably no man living has ever read them, unless for purely critical purposes. But one who had no conception of distinct | developed, especially on the back and the sides of the tail, and impart to the body a certain rigidity which interferes with abruptly sideward motions of the fish. Therefore mackerel generally swim in a straightforward direction, deviating sidewards only when compelled, and rarely turning about in the same spot. They are in almost continuous motion, their power of endurance being equal to the rapidity of their motions. Mackerel, like all fishes of this family (with the exception, perhaps, of Echeneis, which has not yet been examined in this respect), have a firm flesh; that is, the muscles of the several segments are interlaced, and receive a greater supply of blood-vessels and nerves than in other fishes. Therefore the flesh, especially of the larger kinds, is of a red colour; and the energy of their muscular action causes the temperature of their blood to be several degrees higher than in other fishes. But Mackenzie, if nowise a great writer, but quite otherwise essentially a small writer, with a knack of making sentences indeed, but having nothing particular of his own to say, was not therefore altogether a useless man in his day. That he did well for himself, and perhaps for the exchequer too, is quite likely, even though he toiled in the high-Tory service of Dundas, and wrote tracts meant to "broom" out of the country the tide of French Revolutionary notions. At any rate he became in his old age a kind of literary centre and social power in Edinburgh, when that was really needed and useful. He had known John Home and blind Dr Blacklock, and wrote lives of them; but, what is of more consequence, he was among the first to recognize the genius of Robert Burns, as editor of The Lounger, which he and a group of young men with some literary tastes wrote and printed for some years. Yet, though he once breakfasted with Johnson, and certainly met Burns more than once, he has told us nothing about either of them, though a page of Burns's talk would have been worth all The Man of Feeling twice told. It was so far good, however, that he hailed the peasant poet cordially, which we could hardly have hoped so artificial a writer would do, and even better that he noticed the dawn of German literature when Lessing and Schiller rose above the horizon, and not only wrote some account of them, taken from French sources, but boldly set to the study of German that he might really know them at first hand. How far he went in that study we do not know, only he set young Walter Scott on the scent, with results such as he himself could never have imagined. So he lived on, a kind of small king in the Edinburgh literary world, till 1831, dying in his eighty-sixth year, with a wonderful new world around him, which had not yet begun to criticize, but only to admire and honour him. MAČKEREL. Mackerels are pelagic fishes, belonging to a small family, Scombrida, of which the tunny, bonito, albacore, sucking fish (Echeneis), and a few other tropical genera are members (see ICHTHYOLOGY, vol. xii. p. 690). Although the species are fewer in number than in the majority of other families of fishes, they are widely spread and extremely abundant, peopling by countless schools the oceans of the tropical and temperate zones, and approaching the coasts only accidentally, occasionally, or periodically. The mackerels proper (genus Scomber) are readily recognized by their elegantly shaped, well-proportioned body, shining in iridescent colours. Small, thin, deciduous scales equally cover nearly the entire body. The dorsal fin extends over a great part of the back, and consists of several portions: the anterior, composed of feeble spines which can be laid backwards in a groove; the posterior, of rays only, of which the five or six hindmost are detached, forming isolated "finlets." The shape of the anal fin is similar to that of the rayed dorsal. The caudal fin is crescent-shaped, strengthened at the base by two short ridges on each side. The mouth is wide, armed above and below with a row of very small, fixed teeth. No other fish shows finer proportions in the shape of its body. Every "line" of its build is designed and eminently adapted for rapid progression through the water; the muscles massed along the vertebral column are enormously | All fishes of the mackerel family are strictly carnivorous; they unceasingly pursue their prey, which consists principally of other fish and pelagic crustaceans. The fry of clupeoids, which likewise swim in schools, are followed by the mackerel until they reach some shallow part of the coast, which their enemies dare not enter. Mackerels are found in almost all tropical and temperate seas, with the exception of the Atlantic shores of temperate South America, where they have not hitherto been met with. The distinctive characters of the various species have not yet been fully investigated; and there is much confusion in the discrimination of the species. So much is certain that the European mackerel are of two kinds, of which one, the common mackerel, Scomber scomber, lacks, while the other possesses, an air-bladder. The best-known species of the latter kind is Scomber colias, the "Spanish" mackerel;1 a third, Scomber pneumatophorus, is believed by some ichthyologists to be identical with S. colias. Be this as it may, we have strong evidence that the Mediterranean is inhabited by other species different from S. scomber and S. colias, and well characterized by their dentition and coloration. Also the species from St Helena is distinct. Of extra-Atlantic species the mackerel of the Japanese seas are the most nearly allied to the European, those of New Zealand and Australia, and still more those of the Indian Ocean, differing in many conspicuous points. Two of these species occur in the. British seas: Scomber scomber, which is the most common there as well as in other parts of the North Atlantic, crossing the ocean to America, where it abounds; and the Spanish mackerel, Scomber colias, which is distinguished by a somewhat different pattern of coloration, e transverse black bands of the common mackerel being in this species narrower, more irregular or partly broken up into spots, while the scales of the pectoral region are larger, and the snout is longer and more pointed. The Spanish mackerel is, as the name implies, a native of the seas of southern Europe, but single individuals or small schools reach fre quently the shores of Great Britain and of the United States. The home of the common mackerel (to which the following remarks refer) is the North Atlantic, from the Canary Islands to the Orkneys, and from the Mediterranean and the Black Sea and the coasts of Norway to the United States. Towards the spring large schools approach the coasts. Two causes have been assigned of this migration: first, the instinct of finding a suitable locality for propagating their species; and, secondly, the search and pursuit of food, which in the warmer season is more abundant in the neighbourhood of land than in the open sea. It is probable that the latter is the true and only cause, for the following reasons:-mackerel are known to increase much more rapidly in size while in the neighbourhood of land than in the months during which they lead a roving pelagic life in the open sea; and, further, one-year and two-year-old fishes, which have not yet attained maturity, and therefore do not travel land 1 The term "Spanish mackerel " is applied to a very different fish in America, viz., Cybium maculatum. wards for the purpose of spawning, actually take the lead in the migration, and are followed later on by the older and mature fishes. Finally, according to the observations made by Sars, vicinity of land or shallow water are not necessary conditions for the oviposition of mackerel; they spawn at the spot which they happen to have reached during their wanderings at the time when the ova have attained their full development, independently of the distance of the land or of the depth of water below them, as the ova float and the embryo is developed on the surface of the water. In the month of February, or in some years as early as the end of January, the first large schools appear at the entrance of the English Channel, and are met by the more adventurous of the driftnet fishers many miles west of the Scilly Islands. These early schools, which, as we mentioned above, consist chiefly of one-year and two-year-old fishes, yield sometimes enormous catches, whilst in other years they escape the drift-nets altogether, passing them, for some hitherto unexplained reason, at a greater depth than that to which the nets reach, viz., 20 feet. As the season advances, the schools penetrate farther northwards into St George's Channel or eastwards into the English Channel. The fishery then assumes proportions which render.it next in importance to the herring and cod fisheries. In Plymouth alone a fleet of some two hundred boats assembles; and on the French side of the Channel no less capital and labour are invested in it, the vessels employed being, though less in number, larger in size than on the English side. Simultaneously with the drift-net the deep-sea-seine and shore-seine are used, which towards June almost entirely supersede the drift-net. Towards the end of May the old fish become heavy with spawn, and are in the highest condition for the table; and the latter half of June or beginning of July may be regarded as the time at which the greater part of mackerel spawn. Mackerel are scarcely less abundant in the German Ocean; probably some of the schools never leave it, and this resident stock (if we are allowed to apply this term to a fish which is ever shifting its quarters) is increased by the schools coming from the Atlantic through the English Channel or round the north coast of Scotland. The schools approach the coasts of the German Ocean somewhat later in the season, partly owing to the greater severity of the weather, which detains the resident fishes the open sea, and partly owing to the greater distance which the Atlantic shoals have to travel. On the Norwegian coast mackerel fishing does not begin before May, whilst on the English coasts large catches are frequently made in March. Large cargoes are now annually imported in ice from Norway to the English market. After the spawning the schools break up into smaller companies which are much scattered, and offer for two or three months employment to the hand-line fishermen. They now begin to disappear from the coasts and return to the open sea. Single individuals or small companies are found, however, on the coast all the year round; they may have become detached from the main bodies, and be seeking for the larger schools which have long left on their return migration. Although, on the whole, the course and time of the annual migration of mackerel are marked with great regularity, their appearance and abundance at certain localities are subject to great variations. They may pass a spot at such a depth as to evade the nets, and reappear at the surface some days after farther eastwards; they may deviate from their direct line of migration, and even temporarily return westwards. In some years between 1852 and 1867 the old mackerel disappeared off Guernsey from the surface, and were accidentally discovered feeding at the bottom. Many were taken at 10 fathoms and deeper with the line, and all were of exceptionally large size, several measuring 18 inches, and weigh ing nearly 3 b; these are the largest mackerel on record. The mackerel most esteemed as food is the common species, and individuals from 10 to 12 inches in length are considered the best flavoured. In more southern latitudes, however, this species seems to deteriorate, specimens from the coast of Portugal, and from the Mediterranean and Black Sea, being stated to be dry and resembling in flavour the Spanish mackerel (S. colias), which is not esteemed for the table. See also FISHERIES. (A. C. G.) MACKINTOSH, SIR JAMES (1765-1832), publicist, historian, statesman, and philosopher, was born at Aldourie, 7 miles from Inverness, in 1765. He came of old Highland families both through his father and his mother. Of the former, who was an officer in the army, and was mostly on duty abroad, he saw but little, and he spent his early years under the care of his mother and her relatives. At a very early age young James bore the reputation of a prodigy for multifarious reading and learning. His schooling he received at Fortrose, whence he went in 1780 to college at Aberdeen. As a student in the arts faculty there his reading extended far beyond the bounds of the curriculum; but the influence that most powerfully formed his mind was the companionship of Robert Hall, afterwards so famous as a pulpit orator, with whom he ardently beat the usual round of vexed questions. In 1784 he proceeded for the study of medicine to Edinburgh, where he found a still more congenial field for his opening mind, at a time when Hume had been dead just eight years, while Adam Smith, Dr_Black the father of chemistry, Dr Cullen, Robertson, Ferguson, and other eminent men, were resident there. Mackintosh participated to the full in the intellectual ferment, but did not quite neglect his medical studies, and took his degree, though with characteristic unpunctuality he kept the professors waiting for a considerable time on the examination morning. In 1788 Mackintosh removed to London, then agitated by the trial of Hastings and the king's first lapse into insanity. He was much more interested in these and other political events than in his professional prospects; and his attention was specially directed to the events and tendencies which caused or preceded the Revolution in France. In the year of his removal to London his father died, and he succeeded to the family estate, which, being small and burdened, brought very little income; and, as he made no headway in his profession, his financial outlook was not very bright. It was under these circumstances that he wedded his first wife Catherine Stuart. Yet his marriage was a happy event for him. His wife's prudence was a corrective to his own unpractical temperament, and his efforts in journalism soon became fairly profitable. Mackintosh was soon absorbed in the question of the time; and in April 1791, after long meditation, he published his Vindicia Gallica, a reply to Burke's Reflections on the French Revolution. It was the only worthy answer to Burke that appeared. It placed the author in the front rank of European publicists at the age of twenty-five, and won him the friendship of some of the most distinguished men of the time, including Burke himself. About the same time he became honorary secretary of the association of the Friends of the People. The success of the Vindicia finally decided him to give up the medical for the legal profession. He was called to the bar in 1795, and gained a considerable reputation there as well as a tolerable practice. During this period his greatest public efforts were his lectures (1799) at Lincoln's Inn on the law of nature and nations, of which the introductory discourse was published, and his eloquent defence (1803) of Jean Peltier, a French refugee, tried at the instance of the French Government for a libel against the first consul. In 1804 he was created knight, and received the post of recorder at Bombay, where he spent the next seven years of his life. The spoilt child of London society was not at home in Bombay. He did seek to interest himself in India, and in imitation of Sir William Jones founded the Literary Society of Bombay; but the current literature of Europe was far more engrossing than the old Indian life, and the packet with the latest tidings from Europe and the newest development of the Napoleonic drama was infinitely more interesting than either. In spite of his scholarly and historic sympathies, his heart always was with the new era, and he was glad to return to England, where he arrived in 1812. True to his old faith, he courteously declined the offer of Perceval to resume political life under the auspices of the dominant Tory party, though tempting prospects of office in connexion with India were opened up. He entered parliament in the Whig interest as member for Nairn. He sat for that county, and afterwards for Knaresborough, till his death. In London society, and in Paris during his occasional visits, he was a recognized favourite for his genial wisdom and his great conversational power. On Madame de Stael's visit to London he was the only Englishman capable of representing his country in talk with that phenomenal | Great Britain has produced, was the son of a clergyman, woman. His parliamentary career was marked by the and born at Kilmodan, Argyllshire, in 1698. At the same wide and candid liberalism as his private life. He early age of eleven years he entered the university of opposed the repressive and reactionary measures of the Glasgow, where he graduated as master of arts in his Tory Government, supported and afterwards succeeded sixteenth year. While at the university he exhibited a Romilly in his efforts for reforming the criminal code, and decided genius for mathematics, more especially for took a leading part both in Catholic emancipation and in geometry; and it is said that before the end of his sixthe Reform Bill. But he was too little of a partisan, too teenth year he had discovered many of the theorems afterwidely sympathetic and candid, as well as too elaborate, towards published in his Geometria Organica. be a telling speaker in parliament, and was consequently surpassed by more practical men whose powers were incomparably inferior. From 1818 to 1824 he was professor of law and general politics in the East India Company's College at Haileybury. In the midst of the attractions of London society and of his parliamentary avocations Mackintosh felt that the real work of his life was being neglected. His great ambition was to write a history of England. His studies both in English and foreign speculation led him to cherish the design also of making some worthy contribution to philosophy. There is real pathos in the fact that it was not till 1828, when he was sixty-three years of age, and even then only at the instance of Macvey Napier, editor of the Encyclopædia Britannica, that he set about the first task of his literary ambition. This was the Dissertation on the Progress of Ethical Philosophy, prefixed to the seventh edition of the Encyclopædia. The dissertation, written mostly in ill-health and in snatches of time taken from his parliamentary engagements, was published in 1831. About the same time he wrote for the Cabinet Cyclopædia a "History of England from the Earliest Times to the Final Establishment of the Reformation." His more elaborate History of the Revolution, for which he had made great researches and collections, was not published till after his death. Already a privy councillor, Mackintosh was appointed commissioner for the affairs of India under the Whig administration of 1830. He died in 1832. Mackintosh was undoubtedly one of the most cultured and catholic-minded men of his time. His studies and sympathies embraced almost every human interest, except pure science. But it was the width of his intellectual sympathies joined to a constitutional indecision and vis inertia that prevented him from doing more enduring work. Thus it was that his actual achievements came so far short both of his real power and of the promise given in his early efforts. The works of Mackintosh which have the best claim to permanent value are the Findicia Gallicæ, the Dissertation, and the History of the English Revolution. Of the three the first is the greatest both in ability and historical significance. It is the verdict of a philosophic Liberal on the development of the French Revolution up to the spring of 1791, and is at the same time a sympathetic estimate of its causes, principles, and tendencies. While respectful to his great opponent, he is firm and manly in his assertion of the rights and interests of man so deeply concerned in the Revolution. Its excesses compelled him a few years after to express his entire agreement with the opinions of Burke; but few will now deny that his early judgment was the more correct. The Dissertation is a sketchy and fragmentary work, redeemed by catholic criticisin and ingenious suggestion. It was a great undertaking, for which half a lifetime would hardly have been sufficient, attempted at a time when the study of the history of philosophy had hardly been begun. Yet his suggestions as to the formation of conscience are valuable. The History of the Revolution in England in 1688, which is only a posthumous fragment of a long meditated history of England beginning with the Revolution, is written in a style of calm and lofty impartiality. It is wanting in colouring, in movement, in the concrete and picturesque, and could never have been a popular history. It gives the history only of three years (1685-88), breaking off at the point where William of Orange is preparing to intervene in the affairs of England. The account of the early career of the prince is a noble and striking piece of work, showing that, if the author could have resisted the charms of society and applied himself resolutely to historical composition, he might have achieved something really great in that department. See the Memoirs of Sir James Mackintosh's Life, edited by his son; also Macaulay's Essay on Sir J. Mackintosh. MACLAURIN, COLIN (1698-1746), one of the most eminent among the mathematicians and philosophers that In In 1717 he was elected professor of mathematics in Marischal College, Aberdeen, as the result of a competitive examination. Two years later he was admitted a fellow of the Royal Society, and in a visit to London made the acquaintance of Newton, whose friendship and esteem he afterwards enjoyed. In 1719 he published his Geometria Organica, sive descriptio linearum curvarum universalis. This work was inspired by the beautiful discoveries of Newton on the organic description of conic sections. it Maclaurin introduced the well-known method of generat ing conics which bears his name, and showed that many species of curves of the third and fourth degrees can be described by the intersection of two movable angles. In 1721 he wrote a supplement to the Geometria Organica, which he afterwards published, with extensions, in the Philosophical Transactions for 1735. This paper is principally based on the following general theorem, which is a remarkable extension of Pascal's hexagram :—“ If a polygon move so that each of its sides passes through a fixed point, and if all its summits except one describe curves of the degrees m, n, p, &c., respectively, then the free summit moves on a curve of the degree 2mnp. which reduces to mnp. when the fixed points all lie on a right line." In 1722 Maclaurin travelled as tutor and companion to the eldest son of Lord Polwarth, and after a short stay in Paris resided for some time in Lorraine, where he wrote an essay on the percussion of bodies, which obtained the prize of the French Academy of Science for the year 1724. The following year he was elected professor of mathematics in the university of Edinburgh on the urgent recommendation of Newton. After the death of Newton in 1728, his nephew, Mr Conduitt, applied to Maclaurin for his assistance in publishing an account of Newton's life and discoveries. This Maclaurin gladly undertook, but before the account was written the death of Mr Conduitt put a stop to the project. It was not until many years afterwards, and subsequently to Maclaurin's death, that this account of Newton's philosophical discoveries was published (1748). In 1740 Maclaurin obtained the high distinction of dividing with Euler and Daniel Bernoulli the prize offered by the French Academy of Science for an essay on the flux and reflux of the sea. This important memoir was subsequently revised by him, and inserted in his Treatise on Fluxions, which was published at Edinburgh in 1742, in two volumes. In the preface he states that the work was undertaken in consequence of the attack on the method of fluxions made by Berkeley in 1734, under the title of The Analyst. trine of fluxions on geometrical demonstration, after the Maclaurin's object was to found the docmanner of Archimedes and the ancient mathematicians, and thus to answer all objections to its method as being founded down the grounds of the fluxional method, regarding on false reasoning and full of mystery. He thus laid fluxions as velocities, after Newton. He proceeded to give an extensive application of the method to curves, surfaces, and the other subjects usually discussed in works on the differential and integral calculus, his treatment being almost exclusively geometrical; but the most valuable part of the work is that devoted to physical applications, in which he embodied his essay on the tides, as stated above. 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 revolution. 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 Clairaut, 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 discoveries 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'œuvre de géométrie qu'on peut comparer à tout ce qu' Archimède nous a laissé de plus beau et de plus ingénieux" (Mém. de l'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 invitation 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 Anne, 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 discoveries was published, and also his algebra in 1748. As an appendix to the latter appeared his work, De linearum geometricarum proprietatibus generalibus tractatus, 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 competition with the great mathematicians of the Continent at the time, his important discoveries. Among his publications in the Philosophical Transactions the following should be noticed: and his name will ever be held in remembrance in connexion with (1) "Tractatus de curvarum constructione et mensura, ubi plurimæ. series curvarum infinitæ vel rectis mensurantur, vel ad simpliores curvas reducantur," May 1718. The series of curves here treated are what are now styled "pedal" curves, which hold an important place in the modern discussion of curves. Maclaurin established many geometrical properties connecting a curve with its pedal. He investigated 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 describendi French translations of his Treatise on Fluxions and that on M'LENNAN, JOHN FERGUSON, LL.D. (1827-1881), one of the most original of modern inquirers into the constitution 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 Relationship," 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. 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. He 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 truth, by a warm and affectionate disposition, and by his From |