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um (masters of the liberal arts)—a title with which that of doctor of philosophy was afterwards joined. As the origin of this dignity is more ancient than that of doctor, it is still placed before it in most of the German universities. The precise period of its introduction is not known; but even in the twelfth and thirteenth centuries, the honor was so highly esteemed in France, that the most distinguished men were eager to obtain it. Since that time, its dignity has been greatly diminished. This title is to be distinguished from the magister legens, that is, one who has obtained the right, by public disputations, to deliver lectures. In the English and American universities, the title of master of arts is intermediate between those of bachelor of arts and doctor.

MASTER OF THE HORSE (magister equitum); the commander of the cavalry among the Romans. He was among the high extraordinary magistrates, and was appointed by the dictator immediately after his own election. He was next to the dictator in rank, in the army, and had almost the same insignia with him. He was also permitted to mount his horse in the city.

MASTER OF THE ORDNANCE; a great officer, who has the chief command of the king's ordnance and artillery.

MASTER OF THE ROLLS; a patent officer for life, who has the custody of the rolls of parliament, and patents which pass the great seal, and of the records of chancery, &c. In the absence of the chancellor, he sits as judge in the court of chancery; at other times, he hears causes in the rolls chapel, and makes orders; he has a writ of summons to parliament.

MASTER-SINGERS. 'Between the slavery of the Eastern castes, which bind men immutably to the occupations of their fathers, and the perfect freedom of pursuit with us in the West, stand, as it were, the corporations of the middle ages. The lawlessness of the times compelled men of the same occupation to unite in societies for their mutual protection; and, being so united, their disgust at the wild disorder of the period led them to subject themselves to rules even of a minute and pedantic strictness. These habits of constraint extended their influence beyond the useful arts to the fine arts, and even to poetry itself. In the thirteenth century, poetry was a favorite occupation at courts and among the knights; but, with the beginning of the fourteenth century, this peaceable disposition ceased almost encirely, and incessant feuds almost every

It

where ensued. Industry and the arts, however, grew up behind the walls of the cities (q. v.), and the corporations of citizens were established. During the long evenings of winter, the worthy burghers of the German cities assembled to read the poems of the minstrels. Some of the hearers were naturally led to try their own skill in verse; others followed; and the spirit of the age soon imbodied these votaries of the muse in corporations, or, at least, societies after the fashion of corporations. Like the other corporations, they laid claim to a very early origin. is well settled that the emperor Charles IV gave them a charter and a coat of arms. They generally called 12 poets, mostly of the time of the war on the Wartburg (q. v.), their masters; hence their name master-singers. They preferred, however, the more modest name of friends of the master song. They met at certain days, and criticised each other's productions, in which external correctness seems to have appeared to them the chief object; few, indeed, had an idea of the difference between poetical and prosaical ideas or expressions. Their attempts in the lyric style were limited to spiritua songs; in the epic, to rhymed versions of the scriptural narratives. They were also fond of the didactic style. The rules by which the members of the societies were to be guided, as to the metre, &c., of their compositions, were written on a table, anu called Tabulatur, for the sake of enforcing a strict observance of purity in language and prosody: the chief faults to be avoided were collected; they were 32 in number, and distinguished by particular names. He who invented a new metre, invented also a new tune; the names of which were the drollest, and sometimes the most senseless imaginable. Besides their stated meetings, they held public meetings, generally on Sundays, and festivals in the afternoon, in churches. In Nuremberg, where the master-singers flourished particularly, such meetings were opened with free-singing, in which any body might sing, though not belonging to the corporation. In this, the choice of the subjects was left comparatively uncontrolled; ther followed the chief singing, when only those who belonged to the corporation were allowed to sing, and only on Scriptural subjects. The judges were called Merker, and sat behind a curtain. There were four: one watched whether the song was according to the text of the Bible, which lay open before him; the second, whether the prosody was correct;

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its port on the Meuse, and regular packetboats ran to Liege and other places on the river. (For the effects of the Belgian revolution on this navigation, see Netherlands.) Mastricht has been rendered famous by the numerous sieges which it has sustained. In 1673 and 1748, it was taken by the French, who bombarded it without success in 1793, and again captured it in 1794.

MATADOR (Spanish, one who kills). This word is used in some games with cards. In ombre and quadrille, it signifies one of the three principal cards, which are always the two black aces, the deuce in spades and clubs, and the seven in hearts and clubs. This application is probably taken from the Spanish bullfights (q. v.), in which the man who gives the deadly blow to the bull is called el matador. Others derive the name from a band of volunteers, who were established by the inhabitants of Barcelona, when they fought against Philip V, and whose duty was to punish with death those who murmured against the government.

MATANZAS; a seaport on the coast of Cuba, 30 leagues from the coast of Florida, and 20 from Havana; lon. 81° 36′ W.; lat. 23° 2 N.; population, 11,341, or, including the garrison and strangers, 14,340; 1941 free blacks, 3067 slaves. It is situated on a bay of the same name, which affords one of the largest, safest, and most convenient harbors in America, having a good castle for its defence. It has considcrable commerce, exporting sugar, molasses and coffee. The situation is healthy. MATAPAN CAPE (anciently Tænarum). This cape and Malea, or cape St. Angelo, are the two most southern capes of the Morea, the former in lat. 36° 23' 20'' N.; lon. 22° 29′ 38′′ E.: the latter in lat. 36°25′ N.; lon. 23° 12′ 8′′ E.

MATERIA MEDICA. (See Medicine.) MATERIAL and MORAL; two terms used in military language, and derived from the French. The former means every thing belonging to an army except the men and horses; the latter means the spirit of the soldiery, as to cheerfulness, courage, and devotion to their cause. Thus t is said: Though the material of the army was in a wretched condition, yet in respect to its moral, it was superior to the enemy. MATERIALISM, in philosophy; that docirme which considers matter or corporeal substance the primitive cause of things. He who adopts this doctrine is called a materialist. In respect to psychology, in particular, materialism means the doctrine that the soul is a material substance. Ma

terialism is opposed to the doctrine of the spiritual nature of the soul, or immaterialism. Both may be either empirical or transcendental. Materialism is of the first sort, if it founds all its positions and reasonings on experience derived from the sensual world, and therefore strives to explain the internal phenomena from the external; it is transcendental, if it looks beyond experience. Materialism differs according as it considers matter merely, or matter in an organized shape, as the original existence, and in the first case sometimes adopts an ethereal matter, an invisible fluid, sometimes the light, water, &c., as the primitive substance. It also differs according to the hypotheses by which it explains the origin of things. In regard to the soul, the materialist maintains that matter produces in itself spiritual changes, or that the soul is a consequence of the whole bodily organization, by which matter is refined and ennobled into mind. Among the advocates of this doctrine' we may mention Priestley. This theory, however, does not explain how matter can think, and how physical motion can produce mental changes, which we do not observe in so many organic beings; how, in particular, a notion of its own activity can originate. Numerous auxiliary hypotheses, therefore, have been devised, as that of the vibration of nerves by Hartley. In decided opposition, however, to materialism, is our consciousness of the identity and liberty of man, which would be annihilated by it, because matter is governed by the necessity of nature, and free will therefore excluded. Materialism is a very ancient view of nature, and the predominant one in the most ancient Greek philosophy, poetry and mythology, surrounded, however, by all the graces in which the poetical spirit of this imaginative people could array it.

MATHEMATICAL GEOGRAPHY is the application of mathematics and astronomy to the measurement of the earth. The ancients had made no inconsiderable progress in this science. This science starts from two principles: 1. that the earth is to be considered as a sphere; and, 2. that the points and circles, imagined on the heavens, correspond with points and circles on the earth. (See Earth, Pole, Equator, Tropics, Meridians, Degree, Latitude, &c.; see, also, Geography.)

MATHEMATICS. If we call every thing, which we can represent to our mind as composed of homogeneous parts, a magnitude, mathematics, according to the common definition, is the science of

determining magnitudes, i. e. of measuring or calculating. Every magnitude appears as a collection of homogeneous parts, and may be considered in this sole respect; but it also appears under a particular form or extension in space, which originates from the composition of the homogeneous parts, and to which belong the notions of situation, proportion of parts, &c. Not only all objects of the bodily world, but also time, powers, motion, light, tones, &c., may be represented and treated as mathematical magnitudes. The science of mathematics has to do only with these two properties of magnitudes, the quantity of the homogeneous parts, which gives the numerical magnitude, and the form, which gives the magnitude of extension. This is one way, and the most common, of representing the subject: there are others more philosophical, but less adapted to the limited space which can be allowed to so vast a subject, in a work like the present. In investigating these two properties of magnitudes, the peculiar strictness of the proofs of mathematics gives to its conclusions and all its processes a certainty, clearness and general application, which satisfies the mind, and elevates and enlarges the sphere of its activity.* (See Method, Mathematical.) According as a magnitude is considered merely in the respects abovementioned, or in, connexion with other circumstances, mathematics are divided into pure and applied. Pure mathematics are again divided into arithmetic (q. v.), which considers the numerical quality of magnitudes, and geometry (q. v.), which treats of magnitudes in their relations to space. In the solution of their problems, *As a branch of intellectual culture, mathematics has great excellences and great defects. Its certainty, the precision of its signs never conveying more nor less than the meaning intended,its completeness in itself, and independence of all other branches, distinguish it from every other science, and nothing accustoms the young mind more to precision and exactness of thought and expression than the study of mathematics. But, on the other hand, these very excellences render it liable to give a partial direction to the mind, to withdraw it from, and unfit it for pursuits of a different character. Hence so many great mathematicians have appeared to be wholly unfitted for other studies. On the whole, however, its advantages are so great that it can never be dispensed with in a liberal education. Nothing expands and elevates the mind more than the acquisition of a mathematical truth, a law which is obeyed throughout the universe. The study of the conic sections, as has been already observed (see Cone), affords a fine illustration of this in

Bluence. And there are few instances in which

there will be much danger of the pupil being unduly absorbed in the study.

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the common mode of numerical calculation, and also algebra (q. v.), and analysis (q. v.), are employed. To the applied mathematics belong the application of arithmetic to political, commercial and similar calculations; of geometry to surveying (q. v.), levelling, &c.; of pure mathematics to the powers and effects, the gravity, the sound, &c., of the dry, liquid and aeriform bodies in a state of rest, in equilibrium or in motion, in one word, its application to the mechanic sciences, (see Mechanics, Hydraulics, Hydrostatics, &c.); to the rays of light in the optical sciences (see Optics, Dioptrics, Perspective, &c.); to the position, magnitude, motion, path, &c., of heavenly bodies in the astronomical sciences (see Astronomy), with which the measurement and calculation of time (see Chronology) and the art of making sun-dials (see Dial) are closely connected. The name of applied mathematics has sometimes been so extended as to embrace the application of the science to architecture, navigation, the military art, geography, natural philosophy, &c.; but in these connexions it may more conveniently be considered as forming a part of the respective sciences and arts. It is to be regretted that there is as yet no perfectly satisfactory work, treating of the history of this science, so noble in itself, and so vast in its application: even Kästner and Montucla leave much to be desired. The establishment of mathematics on a scientific basis probably took place among the Indians and Egyptians. The first developement of the science we find among the Greeks, those great teachers of Eurone in almost all branches. Thales, and no. particularly Pythagoras, Plato, Eudoxus, investigated mathematics with a scientific spirit, and extended its domain. It appears that geometry, in those ages, was more thoroughly cultivated than arithmetic. The ancients, indeed, under stood by the latter something different from that which we understand by it. In fact, we have not a clear idea of the ancient arithmetic. Their numerical calculation was limited and awkward, sufficient ground for which might be found in their imperfect way of writing numbers, if there was no other reason. Euclid's famous Elements, a work of unrivalled excellence, considering the time of its origin, the ingenious discoveries of Archimedes, the deep investigations of Apollonius of Perga, carried the geometry of the ancients to a height which has been the admiration of all subsequent times. Since then it has been made to bear more on