PAPYROGRAPHY PARABOLA. 



411 



and exclaimed, when he heard that Gustavus had 

 also fallen, " Let the duke of Friedland (Wallenstein) 

 know that I am mortally wounded ; but I depart with 

 joy, as I know that the implacable enemy of my faith 

 has fallen with me on the same day. 



PAPYROGRAPHY (so called by Mr Sennefel- 

 der) ; the art of taking impressions from a kind of 

 pasteboard, covered with a calcareous substance 

 (called lithographic paper), in the same manner as 

 stones are used in the process of lithography. It is 

 an art but lately invented. See Sennefelder's Pa- 

 pyrographische Sammlung. 



PAPYRUS (cyperua papyrus of Linnaeus). This 

 sedge-like plant has acquired celebrity from its fur- 

 nishing the paper of the ancient Egyptians. The 

 root is very large, hard, and creeping ; the stem is 

 very stout, naked, except at the base, eight or ten 

 feet higli ; triangular above, and terminated by a 

 compound, wide-spreading and beautiful umbel, which 

 is surrounded with an involucre composed of eight 

 large sword-sharped 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 ob- 

 served it in the Jordan, and in two places in Upper 

 and Lower Egypt. It now grows wild in Sicily, and 

 late travellers have discovered it in some of the west- 

 ern rivers of Africa, which circumstance renders it 

 probable that it is found throughout the greater por- 

 tion of the interior of that continent. 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 sub- 

 stance, 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 manu- 

 facture of paper, by a process which has been known 

 from the remotest antiquity, even before the historical 

 times of Greece. (For this, see Paper.) In order to 

 raise the plant in our green-houses, it is necessary to 

 place it in a cistern of water, having rich mud at the 

 bottom. 



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 Greek preposition of very various 

 meaning, according to the case which it governs. 

 In compound words, it means above, aside, against, 

 about, thereto, &c., and it appears in a very large 

 number of our compound words. 



PARA ; a Turkish coin, very thin and small, of 

 copper and silver, the fortieth part of a Turkish 

 piaster, which is constantly varying in value, some- 

 times fourteen of them being equal to a Spanish 

 dollar, sometimes fifteen, &c. It is as light in weight 

 as it is of little value, and the writer well recollects 

 its liability to be blown away in making payments in 

 the open air in a windy day. The Greek phwnix 

 is the sixth part of a Spanish dollar. 



PARABAS1S; a transition, fault, extravagance; 

 particularly a part of the ancient comedy, in which 

 the poet himself addresses the spectators, through 

 the leader of the chorus. 



PARABLE (from the Greek, <raja0xi) ; some- 

 times a mere simile, but usually a scries of them, 





or a tale made up of similes. The parable differs 

 from the allegory by the circumstance of being less 

 symbolical. The original idea is not keptrso com- 

 pletely out of sight. From the fable proper it differs 

 by being taken from the province of reality. Fine 

 parables are contained in the Old and New Testa- 

 ment ; this mode of instruction, in fact, is very 

 common with the Eastern nations ; e. g. the parable 

 which Nathan addressed to David, Christ's parable 

 of the prodigal son, of the labourers in the vineyard, 

 of the faithless steward. Herder and Krummacher 

 have distinguished themselves among the German 

 writers by their parables. 



PARABOLA; a curve, formed by that section of 

 a cone in which the axis of the section is parallel 

 with the opposite side of the cone. The following i 

 an easy method of drawing the parabola. Let AB 

 be a right line, and C K ,_ 



a point without it, and 

 DKF a square in the 

 same plane with the 

 line and point, so that 

 one side, as DK, be ap- 

 plied to AB, and KF 

 coincide with the point 

 C ; on F, fix one end of 

 the thread FNC, and 

 the other at the point 

 C ; and let part of the 

 thread, as FN, be brought to the side KF by a pin 

 N ; then let the square DKF, be removed from B 

 to A, applying its side DK close to BA ; and in 

 the mean time the thread will be always applied to 

 the side KF ; and by the motion of the pin N there 

 will be described a curve called a semi-parabola. Then 

 bringing the square to its first position, moving from 

 B to H B the other semi-parabola will be described. 



The point, where the side of the cone is intersected 

 by the plane, is called the apex. All the parallel 

 lines which are drawn within the curve perpendicu- 

 larly through the axis (which runs from the apex 

 through the surface of the curve), are called ordi- 

 nates ; the halves into which the axis is divided, 

 semiordinates : the portion of the axis from the apex 

 to its point of intersection with a given ordinate, 

 the abscissa of that ordinate ; the two sides of the 

 curve, from the apex to the base of the cone, the legs 

 of the parabola. The length of the legs varies with 

 the distance of the section from the vertex of the 

 cone. The distance of its apex from the vertex of a 

 given cone determines its curvature. The square of 

 the semiordinate in the parabola is equal to the 

 rectangle of the abscissa of the semiordinate and of 

 the parameter, a line which is to the distance of the 

 apex from the vertex of the cone as the square of 

 the diameter of the base is to the square of the side 

 of the cone. The magnitude of the parameter is 

 always the same for any given distance of the apex 

 from the vertex, and consequently for any given 

 parabola ; but the semiordinates and their abscissas 

 are longer in proportion as the latter are farther 

 from the apex. If the side of the cone and the 

 diameter of its base, and consequently also their 

 squares, are equal to each other, the parameter is 

 equal to the distance of the apex from the vertex of 

 the cone ; or, in other words, this distance itself is 

 the parameter. The point in the axis where the 

 abscissa is equal to the parameter, is called the 

 focus. It bears this name, because the theory of the 

 parabolic concave mirror is founded upon its prin- 

 cipal property. The theory of the parabola is not 

 less important in the science of gunnery. Every 

 projectile, which does not fall perpendicularly, 

 moves in a direction resulting from the force cf pro- 

 jection and the gravitation of the projectile, and 



