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PERKINS 189 PERPENDICULAR PERKINS, JAMES BRECK, an American lawyer and historical writer; born in St. Croix Falls, Wis., Nov. 4, 1847. Congressman 1902-1905. His chief works are : "France under Mazarin" (1886) ; "France under the Regency" (1892) ; "France under Louis XV.," etc. He died Mar. 11, 1910. PERLITE, a variety of obsidian with an enamel-like luster and a gray color. Structure, usually granular, fine to coarse-grained, occasionally spherulitic. Sub-translucent to opaque. PERM, a city of Russia, the capital of the former government of the same name. Prior to the World War there were important manufactories of tan- neries and the port had considerable trade. Pop. about 65,000. PERMANGANATE, a compound of permanganic anhydride, Mn^Or, and a base. Potassic permanganate is used as a disinfectant, and as a chemical reagent. PERMIAN PERIOD, the name given to the closing era of the Carboniferous age, which was a time of decline for Palaeozoic life, and of transition toward a new phase of geological history. In the United States the Permian rocks are confined to the interior continental basin, and occur in the portion of it W. of the Mississippi, especially in Kansas. The rocks are limestones, sandstones, red, greenish, and gray marls or shales, gyp- sum beds and conglomerates, among which the limestones in some regions pre- dominate. The Permian period was so called by Murchison, because he found them largely developed in that portion of Russia which composed the an- cient kingdom of Permia, of which the actual government of Perm forms a part. PERMUTATION, the act of exchang- ing one thing for another; mutual change ; interchange ; intei'mutation. Also in mathematics, change or combina- tion of any number of quantities. The different arrangements which can be made of any number of given quantities, vvhen a certain number, or the whole of them, are taken together; thus the per- mutations of a, b, and c, taken two to- gether, are ab, ac, ba, be, 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. PERNAMBUCO, a town in Brazil, capital of the province of the same name, on the E. coast. It consists of three dis- tinct parts: Recife, occupying a small Vol. VII— Cyc peninsula; Sao Antonio, on an island; and Boa Vista, on the mainland, the three parts being connected by iron 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 resi- dential quarter. The principal expoi'ts are sugar and cotton; and the chief im- ports Manchester goods and hardware. Pernambuco was founded by the Portu- guese in the 16th century. From 1630 to 1654 it was in the hands of the Dutch, 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 culti- vated crops are the sugar cane and cot- ton ; the forests yielding valuable timber, including Brazil wood, often called Per- nambuco wood. PERONNE, a fortified town in France, on the Somme, 94 miles N. of Paris, nota- ble only on account of being the center of heavy fighting during the World War, especially during the great German offensive in the spring of 1918. (See PiCARDY, Battles of.) Here, on March 24, 1918, the British were heavily at- tacked by the Germans and driven back. Though a failure in its main objective, the German offensive succeeded in gain- ing a considerable area of territory, in the form of a wide salient, of which Peronne was in the center. PEROXIDE, a term applied in mineral chemistry to certain dioxides in which the second atom of oxygen is held in a state of weak combination, as in the case of barium peroxide, BaO... By the ac- tion of strong sulphuric acid, barium sul- phate is formed and oxygen set free. In organic chemistry it applies to certain peroxides or organic radicals, produced by the action of barium peroxide on the anhydride of the radical. Acetic anhy- dride is by this means converted into C=H.O I peroxide of acetyl, rO-. C^HaO J PERPENDICULAR, in geometry, a line falling directly on another line, so as to make equal angles on each line. A 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- gent with the curve. In this case the perpendicular is usually called a normal to the curve. 13