Permutation
the act of exchanging one thing for another; mutual intermutation. change; interchange; inte Also in mathematics, change or combination of any number of quantities. The different arrangements which made of any number of given quantities, when a certain number, or the whole of them, are taken together; thus the permutations of a, b, and c, taken two together, are ab, ac, ba, bc, ca, and cb. The number of permutations of n things taken two together is n (n-1); of n things taken three together, n(n-1) (n-2), and so on.
Only in Collier's New Encyclopedia
Permutations
in mathematics, the number of groups that can be formed with a given number of units, taking order into consideration. With a and b but one combination, ab; can be formed, but two permutations, ab and ba, are possible. Both of these permutations are the same combination. If three elements, a, b, and c, be taken we may have four combinations, ab, ac, bc, and abc; but each of the first three combinations is capable of two permutations, and the last combination is capable of six permutations, namely, abc, acb, bac, bca, cab, cba. The number of possible permutations with a given number of units forms a chapter in higher algebra.
Only in Aiton's Encyclopedia
Pernambuco
a town in Brazil, capital of the province of the same name, on the E. coast. It consists of three distinct parts: Recife, occupying a small Vol. VII-Cyc JAMES BRECK, an peninsula; São Antonio, on an island; and Boa Vista, on the mainland, the being connected by iron three parts be ts bridges. Recife is the principal seat of business. In it are the custom house, the exchange, a marine arsenal, etc. San Antonio has broad streets and many fine houses, and contains the episcopal palace, the theater, the military arsenals, etc. Boa Vista is the fashionable residential quarter. The principal exports and cotton; and the chief imports Manchester goods and hardware. are sugar Pernambuco was founded by the Portuguese in the 16th century. From 1630 hands of the Dutch, to 1654 it was in the under whom it prospered greatly. It is now the third largest city in Brazil, and the second in commercial importance. Pop. about 220,000. The province has an area of 49,625 square miles. Pop. about 2,100,000. The principal cultivated crops are the sugar cane and cotton; the forests yielding valuable timber, including Brazil wood, often called Pernambuco wood. PÉRONNE, a fortified town in France, on the Somme, 94 miles N. of Paris, notable only on account of being the center of heavy fighting during the World the great German War, especially during ing offensive in the spring of 1918. (See
Only in Collier's New Encyclopedia
Pernety, Antoine Joseph
Author of the Dictionnaire Mytho-Hermétique and Les Fables Egyptiennes et Grecques. According to him the Golden Fleece , in the Jason Medea legend, is symbolical. The labours of Jason represent strivings towards perfection.
Only in An Encyclopaedia of Occultism
Peroxide
a term the second atom of oxygen is held in a state of weak combination, as in the case of barium peroxide, BaO2. By the action of strong sulphuric acid, barium sulphate is formed and oxygen set free. In ong su organic chemistry it applies to certain peroxides or organic radicals, produced by the action of barium peroxide on the anhydride of the radical. Acetic anhycan be dride is by this means converted into } C2H3O peroxide of acetyl, -02. C2H3O
Only in Collier's New Encyclopedia
Perpendicular
in geometry, a line falling directly on another line, so on each line. A as to make equal angles straight line is said to be perpendicular to a curve, when it cuts the curve in a point where another straight line to which it is perpendicular makes a tan- In this case the gent with the curve. perpendicular is usually called a normal to the curve. 13
Only in Collier's New Encyclopedia
Perpendicular Style
the third period of Pointed Architecture. It originated at the end of the 11th century, and continued till the close of the 16th, when it was succeeded by the Revived, or Debased Classic, known as the Elizabethan. It is also known as the Florid, from the multiplicity, profusion, and minuteness of ornamental detail, and its more general name, Perpendicular, is derived from the mullions of the windows and the divisions of ornamental panel work running in straight or pependicular lines, which was not the case in any earlier style. The pointed arches are constructed from almost every radius. The most common doorway is the depressed four-centered arch (almost peculiar to this style) within a square head, having generally a hood molding over, the spandrels being filled with quatrefoils, paneling, roses, foliage, small shields, or other sculptured ornaments. Fan-shaped roofs, ornamented with dependent pendants resembling stalactites, are also peculiar to the Perpendicular style. Richly decorated roof trusses, which are left clearly visible, are also of frequent occurrence. In these roofs the spaces between the highly ornamented and molded beam are filled with rich tracery.
Only in Collier's New Encyclopedia
Perpetual Motion
a motion which, once generated by mechanical means, should have the power of perpetuating itself. A machine which, according to the hopes of its inventors, after it has once set in motion, will keep in motion without drawing on any external source of energy. As early as 1775 the Académie des Sciences of Paris placed the problem in the same category with the duplication of the cube and the quadrature of the circle, and refused to receive schemes claiming to have overcome the difficulty-in reality, to have performed the impossible. The overbalancing wheel was a favorite contrivance with the seekers after a perpetual motion. It appears as early as the 13th century.
Only in Collier's New Encyclopedia
Perpetuity
uninterrupted or continued duration or succession; endless duration; continuance to eternity; something of which there will be no end; that which continues indefinitely. The number of years in which the simple interest of any sum invested in an annuity or annuities becomes equivalent to the principal; also, the amount which will purchase an annuity payable forever. In law, quality or class of an estate by which it becomes inalienable, either perpetually or for an indefinitely long period of time; also, the estate so perpetuated.
Only in Collier's New Encyclopedia
Perpignan
a town of France, and a fortress of the first rank; in the department of Pyrénées-Orientales, on the river Têt, 7 miles from the Mediterranean, 40 S. of Narbonne, and 17 from the Spanish frontier. It commands the passes of the Eastern Pyrénées, and is defended on the S. by a citadel, which incloses the old castle of the Counts of Roussillon, and by a detached fort. The streets are narrow and the houses of semi- Moorish construction, and show evidences of Spanish influence. The cathedral (begun in 1324), the Moorish-Gothic cloth hall or bourse (1396), the town house (1692), the building of the former university (1349-French Revolution), the court house, and a col college are the principal public buildings. Good red wine is made, sheep and silkworms are bred, vegetables and fruit grown, brandy distilled, cloth woven, and corks cut; and there is a good trade in wine, spirits, wool, cork bark, oil, cloth, and silk. As capital of the former county of Roussillon Perpignan was in the hands of the kings of Aragon from 1172 to its capture by France in 1475; it was restored to Spain in 1493; but Richelieu retook it in 1642, and France has possessed it ever since. Pop. (1911) 39,510.
Only in Collier's New Encyclopedia