M A C M A C 161 representing his country in talk with that phenomenal woman. His parliamentary career was marked by the same wide and candid liberalism as his private life. He opposed the repressive and reactionary measures of the Tory Government, supported and afterwards succeeded Romilly in his efforts for reforming the criminal code, and took a leading part both in Catholic emancipation and in the Reform Bill. But lie was too little of a partisan, too widely sympathetic and candid, as well as too elaborate, to be a telling speaker in parliament, and was consequently surpassed by more practical men whose powers were incom parably 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 philo sophy. There is real pathos in the fact that it was not till 1823, when he was sixty- three years of age, and even then only at the instance of Macvey Napier, editor of the Encyclopaedia 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 Encyclopaedia. 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 Cyclopaedia 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 con stitutional indecision and vis inertias, 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 Vindlcise, Gallicas, 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 criticism and ingenious suggestion. It was a great under taking, 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 Great Britain has produced, was the son of a clergyman, and born at Kilmodan, Argyllshire, in 1698. At the early age of eleven years he entered the university of Glasgow, where he graduated as master of arts in his sixteenth year. While at the university he exhibited a decided genius for mathematics, more especially for geometry ; and it is said that before the end of his six teenth year he had discovered many of the theorems after wards published in his Geometria Organica. 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. In it Maclaurin introduced the well-known method of generat ing conies 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 *lmnp .... 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 recommenda tion of Newton. After the death of Newton in 1728, his nephew, Mr Conduitt, applied to Maclaurin for his assist ance 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. Maclaurin s object was to found the doc trine of fluxions on geometrical demonstration, after the manner of Archimedes and the ancient mathematicians, and thus to answer all objections to its method as being founded on false reasoning and full of mystery. He thus laid down the grounds of the fluxional method, regarding 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.
XV. 21