M A T M A T G31 synoptic method, although most branches of applied mathe matics are mixtures using the one or the other, as happens to be convenient. In addition to those already mentioned, we may enumerate the following as among the more im- ; portant departments of applied mathematics: Kirie- j rnatics ; Abstract Dynamics, including Statics and Kinetics whether of a Particle, of a Rigid Solid, of an Elastic Solid, of a Fluid, or of a Chain ; Statistical Mathematics, as exemplified in the Theory of Annuities, and the Kinetic Theory of Gases ; the Mathematical Theory of Diffusion whether of Heat or of Matter ; the Theory of Potential ; and so on. See MECHANICS, HYDROMECHANICS, ANNUI TIES, HEAT, ELECTRICITY, MAGNETISM, &c. The two great methods employed in the investigation of manifoldness must of course be, at bottom, identical ; and every conclusion arrived at by the one must be reach able by the other. The exact nature of the connexion between them will be well seen by studying two instances. Ons of these is the treatment of areas by Euclid and the treatment by the analytical method, which are carefully compared in the article GEOMETRY, vol. x. p. 379. The other is the connexion between the descriptive and the metrical properties of loci. The former include all pro perties such as intersection, tangency, &c., depending on position merely, and are obviously the natural product of the synoptic method. The latter include all relations involving the lengths of lines and the magnitudes of angles, they depend therefore on expression in terms of a unit, and are the natural product of the analytic method. Never theless the analytic method furnishes descriptive properties of loci, and by the introduction of "the absolute" descriptive theorems are made to furnish metrical relations, as has been fully shown by Cayley, Clifford, and Klein (see MEASUREMENT). (G. CH.) MATHER, COTTON (1663-1728), was the most learned and widely known of a family which through four genera tions enjoyed singular consideration, and exercised com manding influence upon New England in its first century. Richard, son of Thomas Mather of Lowton (Winwick), Lancashire, England, after studying for a time at Brasenose, Oxford, and teaching and subsequently preaching at Toxteth Park, went to New England, for nonconformity s sake, in the summer of 1635, where, till his death in 1669, at seventy-three, he was pastor of the Congregational church in Dorchester (now a part of Boston), acquiring large repute, writing three or four instructive and construc tive treatises upon polity, and being much trusted as to the foundations of both church and state. His youngest son Increase took his first degree at Harvard College in o o 1656, at seventeen, returning, after a visit to the old country, in which he served several pulpits, to take at twenty-five the pastorate of the second (or North) church in Boston, which place he held till his death in 1723 at eighty-five, while, in addition, he had been acting, or actual, president of the college most of the time from 1681 to 1701, the author of one hundred and sixty books or tracts, and for four of its most perilous years the choice of all its citizens to represent the Massachusetts colony before the English Government. His wife Maria was daughter of the famous John Cotton, and their first-born received both family names, and when he took his B.A. degree at less than sixteen, at Harvard, in 1678, his promise tempted President Oakes to say in his presence, referring to his two distinguished grandfathers : " Cottonus atque Matherus tarn re quam nomine coalescant et reviviscant." After a short time spent as tutor, and a period of diligent toil end ing in the conquest of an impediment of speech which endangered success in the family profession, he became assistant to his father, in two years being ordained co- pastor, and holding the pulpit for nearly three and forty years, till his death at sixty-five. As a private Christian, from his frank diaries, it is clear that he laboured much with himself, in a single year devoting more than sixty days to fasting and twenty nights to vigil. As a preacher he was conscientious and successful, always diligently study ing his discourses, in one year delivering more than seventy public sermons, with nearly half as many in private houses, sometimes thus "pressing a glorious Christ" through eleven successive days, and, with six competitors by his side, maintaining to the last his hold upon the largest congregation in New England, having about four hundred gifted communicants. As a pastor he was exceptionally laborious, systematically exhorting and praying with his people at their homes, making conscience of spiritualizing every casual interview, and now and then spending days upon his knees with the names of his flock before him to prompt his intercessions for them, and for himself that he might better reach their peculiar need. As a philan thropist, while abundant in personal benefactions, he origin ated more than twenty societies for public charity, bore the cost of a school for Christianizing the negroes, and, at the risk of life, in the face of popular opposition medically led, advocated and vindicated the introduction of inocula tion as a protection against the then terrible ravages of the small-pox. As an author he was learned publishing in French, Spanish, and Algonkin as well as English and voluminous, three hundred and eighty-two of his printed works having been catalogued, several of which are elaborate books, and one a folio of 800 pages ; while his Biblia A?nericana ) by him considered the great work of his life, remains in six huge volumes of manuscript to this day. As a scholar he was better known across the sea than any other American of his time, once contemporaneously corresponding with more than fifty learned Europeans, in his forty-seventh year being made doctor of divinity at Glasgow, and receiving election as a Fellow of the Royal Societyin those days eminent distinctions for a colonist. With all this it must be confessed that he had some grave defects. His common sense was not uniformly equal to his need. Always ambitious and self-opinioned, he was occasionally irritable and conceited. He lacked good taste, and it was his unconcealed grief that he was never elected to preside over Harvard College. His enormous know ledge did not digest well, and his use of learning tended to be crude. He was superstitious, and it was his misfortune that, as to witchcraft, he was not, as with vaccination, in advance of his generation, any more than such men as Richard Baxter and Sir Matthew Hale. Of his works, the Magnolia and Ratio Discipline are indispensable to the student of New England history. MATHEW, THEOBALD (1790-1856), popularly known as Father Mathew, the "Apostle of Temperance," was descended from an illegitimate branch of the Llandaff family, and was born at Thomastown, Tipperary, on October 10, 1790. He received his school education at Kilkenny, whence he passed for a short time to Maynooth ; from 1808 to 1814 he studied at Dublin, where in the latter year he was ordained to the priesthood. Having entered the Capuchin order, he, after a brief time of service at Kilkenny, joined the mission in Cork, which was the scene of his religious and benevolent labours for many years. The movement with which his name is most intimately associated began in 1838 with the establishment of a total abstinence association, which in less than nine months, thanks to his moral influence and eloquence, enrolled no fewer than 150,000 names. It rapidly spread to Limerick and elsewhere, and some idea of its popularity may be formed from the fact that at Nenagh 20,000 persons are said to have taken the pledge in one day, 100,000 at
Galway in two days, and 70,000 in Dublin in five days.