implacable enemy of my faith has fallen with me on the same day.' He died the day after the battle, November 7, 1632.

PAPPUS, ALEXANDRINUS, an eminent mathematician, who flourished at Alexandria towards the end of the fourth century. The accounts of his life are extremely scanty, and all his works appear to have perished, except his Mathematical Collections, which possesses great value, and has sufficed to found his fame. It originally consisted of eight books, of which the whole of the first and about a half of the second are lost, and some of the others are much mutilated. The contents are somewhat miscellaneous, containing, in addition to geometrical problems and theorems, a treatise on mechanics and many interesting notices as to the state of mathematical knowledge at the time. The original Greek has never been printed complete, but there are Latin translations by Commandine (Pesaro, 1588), and by Manolessius (Bologna, 1660). PAPPUS, PROPERTIES OF. See Supplement. PAPUA. See NEW GUINEA

PAPYROGRAPH. See COPYING MACHINES. PAPYRUS (Papyrus antiquorum, the Cyperus papyrus of Linnæus), a plant belonging to the natural order Cyperaceæ. This sedge-like plant has acquired celebrity from its furnishing the paper of the ancient Egyptians. The root is very large, hard, and creeping; the stem is very stout, naked, except at the base, 8 or 10 feet high; triangular above, and terminated by a compound, wide-spreading, and beautiful umbel, which is surrounded with an involucre composed of eight large sword-shaped leaves. The inconspicuous flowers are disposed in little scaly spikelets, which are placed at the extremity of the rays of this umbel. It is an aquatic plant, and the lower part of the stem is always immersed in water. The papyrus grows in the swamps along the borders of the Nile, and not in the stream itself, as has been supposed. Bruce observed it in the Jordan, and in two places in Upper and Lower Egypt. It is now extremely rare in Egypt, but is found growing wild in Sicily, on the banks of the Anapus, near Syracuse, and it has also been discovered in some of the western rivers of Africa. The uses of the papyrus were by no means confined to the making of paper. The inhabitants of the countries where it grows, even to this day, manufacture it into sail-cloth, cordage, and sometimes wearing apparel. Boats are made by weaving the stems compactly together, and covering them externally with a resinous substance to prevent the admission of water. Although these resemble baskets in their appearance, they are of great utility, and indeed are the only kind known in Abyssinia. The roots are also employed for fuel. The most ordinary use, however, was for the manufacture of paper, by a process which has been known from the remotest antiquity, even before the historical times of Greece. In order to raise the plant in our greenhouses, it is necessary to place it in a cistern of water having rich mud at the bottom. (Pl. LXXXI.-II.) PAR (Latin, equal) is used to denote a state of equality or equal value. Bills of exchange, stocks, &c., are at par when they sell for their nominal value; above par or below par when they sell for more or less.

PARA, a Turkish and Egyptian coin, very thin and small, of copper or copper and silver, the fortieth part of a Turkish piastre (grush), which is constantly varying in value. The value of the para is from to of an English penny.

PARA, or GRÃO PARÁ, a maritime province of Brazil, of great size but thinly populated, lying about the lower part of the Amazon, and including Brazilian Guiana, on the north side of that river. It is bounded on the north by British, Dutch, and French Guiana;

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east by the provinces of Maranhão and Goyaz; south by that of Matto Grosso; and west by Alto Amazonas; area, 443,790 square miles. On the northern frontiers are several mountain ranges of considerable height, but the great features by which the province is characterized are its immense plains and the mighty rivers which flow through them. In the eastern part of the province the Tocantins and a number of minor streams carry their waters directly to the ocean, but with this exception all the other rivers are tributaries of the Amazon. The principal of these tributaries are the Negro on the left, the Madeira, Tapajoz, and Xingu on the right bank. The spaces which separate the tributaries from the main stream and from each other are either occupied by tracts of pathless and almost interminable forests, or stretch out into alluvial plains, often clothed with the richest verdure, and almost always of inexhaustible fertility. The climate is remarkably equable, the temperature varying only between about 87° and 100° Fahr. The richness of the soil, seconded by the heat of a tropical sun, produces vegetable forms of gigantic magnitude, from which timber of almost unequalled excellence, both for ordinary and ornamental purposes, is obtained; while even the spontaneous undergrowth furnishes endless varieties of plants and shrubs of the greatest value both in medicine and in the arts. In the comparatively limited tracts which have been brought under cultivation the most important crops are mandioc, rice, millet, coffee, cotton, and sugar-cane. Silkworms are reared; they are fed on the leaves of the orangetree, and yield a silk of a dark yellow colour. In respect of minerals the province, so far as has yet been ascertained, is comparatively poor. Gold and silver, as well as emeralds and other precious stones, occur, but only to a very limited extent. The principal exports are rice, urucu or annotto, a dye said to be preferable to Brazilian wood; cacao, sarsaparilla, caoutchouc and other elastic gums; balsam copaiba, pimento, rum, timber, &c. Population in 1872, exclusive of Indians, 275,237. The Indian population is estimated at about 30,000.

PARA, or BELEM, a city and seaport in Brazil, capital of the province of Pará, on the right bank of the estuary of Rio Pará, where it is entered by the Guama. Pará has straight and mostly paved streets; its houses are of stone, constructed with solidity and some pretensions to elegance. The principal buildings are the governor's palace and the cathedral, magnificent edifices; but besides these the cruciform church of Santa Anna, and the octagonal one of São João Baptista are noteworthy. The city possesses several other churches, a convent turned into a barrack, an arsenal, an Episcopal palace, a seminary in which Latin, theology, &c., are taught; a college with chairs of Latin, rhetoric, philosophy, geometry, and French; a normal and two primary schools, two convents, one of Carmelites and another of Capuchins; three hospitals, and a botanic garden rich in plants both exotic and indigenous. Pará is the seat of the legislative assembly of the province, the residence of the president, of the commander of the forces, and of the Bishop of Pará. The port is defended by forts, and is capable of admitting vessels of any size; the tide rises 10 or 12 feet. The trade of the port is rapidly rising. The principal exports are caoutchouc, cacao, Brazil-nuts, salt, copaiba, rice, piassava, sarsaparilla, annotto, and cotton. The principal disease is intermittent fever. Pop. estimated at from 30,000 to 35,000.

PARABLE, a short tale in which the actions or events of common life are made to serve as a vehicle for moral lessons. The word is derived from the Greek parabole, which literally signifies a throwing

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beside,' and hence a comparison or illustration. In | classical Greek this word parabole is not used in any sense resembling that of our word parable; but by the Hellenistic writers it is used almost invariably as the equivalent of the Hebrew mashal, which, properly meaning similitude, was applied alike to short proverbs, dark prophetic utterances, and tales illustrative of moral truths. It is the word used to designate the parables of Christ by all the evangelists except John, who uses instead paroimia, the literal signification of which is 'something occurring on the common road,' and hence comes to mean a common saying or proverb. The parable differs from the fable proper and from the allegory in being taken from the province of reality, from which the fable departs by attributing to the lower animals and even to inanimate objects the power of speaking and acting like man, and the allegory by representing actors and speakers who are the mere personifications of moral qualities. It differs also from the mythus in being consciously invented for a special purpose, while the mythus grows up unconsciously in popular belief. The parable is a mode of teaching peculiarly adapted to the eastern mind, and was common among the Jews before the appearance of Christ. It is exemplified in the Old Testament in the parable addressed by Nathan to David (2 Sam. xii.), and there are frequent examples of it in the Talmud.

PARABOLA, a conic section. If a right cone is cut by a plane parallel to a slant side, the section is a parabola. It may also be defined as the curve traced out by a point which moves in such a way that its distance from a fixed point, called the 'focus,' is always equal to its perpendicular distance from a fixed straight line, called the 'directrix.' The general equation in x and y of the second degree represents a parabola, when the first three terms form a perfect square. The path of a projectile in vacuo, when not a vertical straight line, is parabolic.

In the figure BH is the directrix, and F the focus of the parabola QDSAP; and, as above stated, FP = PG wherever P may be on the curve. The line FC is drawn through F at right angles to the directrix. This line FC is called the 'axis' of the curve. A, the

'vertex,' is evidently equally distant from F and c. Any line drawn parallel to AF, the axis, is called a 'diameter' of the curve. It has a property peculiar to any 'diameter' of a conic section, namely, that if a chord is bisected by it, it also bisects every chord which can be drawn parallel to the first. If in the figure the curve were produced, we should find it becoming more and more nearly parallel to the axis as it gets further away from the directrix. We shall state a few of the more important propositions regarding the parabola which are to be found in treatises on curves of the second degree.

When the vertex is taken as the origin of co-ordinates, the axis and the tangent at the vertex being taken as axes of co-ordinates, the equation to the curve is given in its simplest form, y = kr. The constant k is called the 'principal parameter' of the diameter, which is the axis of x--that is, the axis of the parabola AF. k is the length of the chord through Fat right angles to the axis, and is evidently equal to

four times AF or AC. If any other point on the curve is taken as origin, the diameter through the point being the axis of x and the tangent being the axis of y, the equation has the same form, y=kx, k being a new constant, called the 'parameter of the diameter,' passing through the origin. A parabola may be considered as an ellipse whose eccentricity is 1. It may be shown that FP and the diameter through P make equal angles with the tangent at P. We thus see that if the parabola rotates about its axis, describing a surface called a 'paraboloid of revolution,' and if this surface is a mirror, rays of light proceeding from the luminous point r are all reflected parallel to the axis.

PARABOLANI, in the early Christian church, a class of men whose chief duty was to attend on the sick and diseased. The name was originally that of the most reckless gladiators, and is derived from the Greek parabolos, desperate.' It is not known when the first fraternities of Christian parabolani were formed, but it is probable that they date from the time of Constantine. It is certain at least that at that epoch there were such functionaries in all the principal churches of the East, but nowhere were they more numerous than at Alexandria, where they formed a corps of 500 men. Theodosius the younger increased this number to 600, because pestilences and contagious diseases were nowhere more common than in Egypt. This emperor placed them under the jurisdiction of the præfectus Augustalis, who was the chief magistrate of the city; but they were appointed by the bishop, whose directions they had to follow in all that concerned their offices of charity. As the parabolani were for the most part bold men, familiar with and indifferent to death, severe laws were enacted with the view of confining them to their duties and preventing them from exciting seditions and disturbances, which were particularly common at Alexandria. By the Theodosian code their number was restricted, and they were forbidden to be present at public assemblies, and even in any court of justice, unless they had some special business there sanctioned by the law. On more than one occasion they showed themselves worthy of the suspicion in which they were held, as for example at the Council of Ephesus in 449, when a Syrian monk named Barsumas, at the head of a band of armed parabolani, committed excesses of the most outrageous kind, and terrified the council into granting all his

demands.

His

PARACELSUS, or PHILIPPUS AUREOLUS THEOPHRASTUS BOMBASTUS VON HOHENHEIM, a celebrated empiric and alchemist, born at Einsiedeln, in the canton of Schwyz, in Switzerland, in 1493. proper name appears to have been Höhener, which became Paracelsus by translation into Greek, in accordance with the common practice of the time. Von Hohenheim was probably an invention of his own. Dissatisfied with the means of acquiring knowledge which were within his reach in his native country, he travelled over the greater part of Europe, including Germany, France, Italy, Spain (visiting Granada, where the Arabs were still credited with knowing more of the mysteries of science than other people), England, and other parts, everywhere seeking to add to his knowledge. In the course of his travels he became acquainted with some remedies not in common use among the faculty (probably preparations of mercury), by means of which he performed extraordinary cures, and obtained great reputation. On the fame of these cures the magistracy of Basel in 1526 offered him the chair of medicine in that city, and the offer was accepted. Here he continued lecturing, sometimes in barbarous Latin, but more commonly in German, till the spring of 1528, when,

a rival in the animal or vegetable world. The food consists chiefly of fruits. The voice of the males is described as loud and piercing, that of the females being of weaker character. The natives of New Guinea kill these birds, and sell the skins and plumage to the Malays, through whom they reach the centres of civilized commerce. They are caught during the night by climbing the trees in which they roost. The specific name apoda of Linnæus was so bestowed from the general belief that these birds wanted feet, although the great naturalist himself was fully aware of these birds possessing limbs. The Superb Bird of Paradise (P. superba) is a familiar species. The P. regia, or King Bird of Paradise, and the P. magnifica and P. viridis, are other species. These birds are said to fly against the wind, so as to avoid ruffling the feathers, and so as to keep them in an expanded state. They are said to fall to the ground when a sudden change of wind occurs.

PARADOX is that which runs counter to general idea and expectation, and appears accordingly to be incredible and incomprehensible. In literature or science we give the name of paradox to any proposition contradictory to what is generally admitted to be the correct view.

PARAFFIN. The name is applied to the solid, fatty, crystalline substance obtained by the destructive distillation of various organic bodies, such as bituminous shale, &c. Paraffin is generally obtained by heating bituminous shale in iron retorts at a low red heat; condensing the tarry products, and purifying these by distillation, washing successively with soda, water, and acid, and again distilling. Those portions of the oil which solidify in the final distillations are collected separately from the liquid portions, washed with soda and acid, and crystallized or again distilled. The partially purified paraffin is now again treated with acid, allowed to solidify, submitted to the action of centrifugal machines, and finally strongly pressed in order to remove any liquid oil which may still adhere to it. The solid substance is now melted and cast into blocks. Large quantities of paraffin are also obtained from American petroleum oil.

The liquid oils obtained in the process sketched above come into commerce under the general name of paraffin-oil, the lighter oils being used for illuminating and the heavier for lubricating purposes.

The amounts of paraffin and of light and heavy oils obtained from 100 parts of different samples of shale are stated in the following table:

The amount of paraffin obtained from the celebrated Boghead cannel or Torbanehill mineral amounted to about 15 parts per 100 of coal.

Pure paraffin has a specific gravity of about 877; it melts about 47, but the melting-point varies in different specimens. Paraffin may be crystallized from an ethereal solution. On account of the great inertness and general inactivity of this substance it has received its name (parum-affinis). Oxidizing agents exert but little action on paraffin, generally speaking; chlorine is without action on it at ordinary temperatures, but if passed into molten paraffin it withdraws a part of the hydrogen, and forms chlorinated derivatives.

From the most recent researches upon the chemical constitution of paraffin it would appear that it is a mixture of hydrocarbons of the marsh-gas or CH2n+2 series with those of the alefine or C. Han series.

The name paraffin is generically applied to all the hydrocarbons of the marsh-gas series. PARAGUAY, a name at one time used in a very extensive sense, so as to include the whole of the immense regions of South America between lat. 16 s. and the Straits of Magellan, and between Chili and Peru on the west, and Brazil on the east, now confined to the republic, extending from lat. 22° to 27° 20′ s., and lon. 54° 40′ to 58° 40' w. Its western boundary is formed by the river Paraguay, which separates it from Bolivia and the Argentine Republic, and its southern and south-eastern by the Paraná, which separates it from the Argentine Republic and Brazil. Its north-eastern boundary, as fixed by the treaty with Brazil of January, 1872, begins in the east at the Salto grande de siete Quedas, on the Paraná, in lat. 24° s., then proceeds up the river Igatim as far as the Serra Maracaju, which it then follows northwards to the sources of the Apa, finally turning west along this river till it joins the Paraguay about lat. 22° s. The area of the state is 56,693 square miles. The whole surface belongs to the basins of the Paraguay and Paraná, a mountain range of considerable elevation stretching between them, north to south, so as to form their watershed, and send the drainage in opposite directions, but nearly in equal portions. The distance of the watershed from the river scarcely anywhere exceeds 100 miles, and hence the tributaries by which the drainage is conveyed are more remarkable for their number than their magnitude. By far the largest is the Tibicuari, which, owing to an eastern bend in the watershed, has its course considerably prolonged, and being augmented by several large affluents from the north, becomes a noble stream before it reaches the Paraguay. From the mountain region the surface rapidly descends, first presenting a finely-diversified succession of lower heights, and then spreading out into rich alluvial plains, which not unfrequently, in the immediate vicinity of the larger streams, are converted into swamps. The climate, though tropical, has its excessive heat greatly modified by the inequalities of the surface, but concurs with the natural fertility of the soil in producing a vegetation of almost unequalled luxuriance and grandeur. In the forests are found at least sixty varieties of timber, admirably adapted for all purposes in which elasticity, durability, or buoyancy is required; dye-woods, gums, drugs, perfumes, vegetable oils, and fruits in almost endless variety. Many of the hills are literally covered with the yerba maté or Paraguay tea (see MATE), no contemptible substitute for the tea of China, and the principal beverage of one-half of South America. The larger plains are roamed over by immense herds of cattle, which, though scarcely required for food in a country otherwise so richly provided, yield valuable products in the shape of hides, tallow, hair, horns, bones, &c.; and on all the alluvial tracts where cultivation is attempted with instruments, however primitive and imperfect, sugar-cane, cotton, tobacco, rice, maize, and in short the greater part of the most valuable products, both of the tropical and the temperate zones, are raised in profusion. A country thus highly favoured by nature, if fully developed, would probably furnish a larger amount of human subsistence than any other tract of equal extent on the surface of the globe. Unfortunately various political causes have seriously interfered with its advancing prosperity.

Paraguay was originally a Spanish colony. The first settlement which they made was in 1535. In 1608 a number of immigrant Jesuits succeeded in obtaining the supreme power in the new colony, and established a powerful and well-organized gov. ernment, which lasted till 1758, when it was over