720 



PKOGNE PROMETHEUS. 



standing \vatrr, as a basis, by a comparison with 

 which, or with its parallels, the angle of every 

 declivity must be determined. Small differences 

 are generally neglected, and the declivity marked 

 only in divisions of five degrees. Major Lehmann, 

 who has highly distinguished himself by his labours 

 in this branch, has gone still further; he has invented 

 a projection, so that what could formerly only be 

 represented by drawing the profile of a mountain, 

 v it. the angle of the declivity, and the kind of troops 

 it will allow to act, is rendered immediately evident 

 by a projection, in which the observer is supposed 

 to be stationed perpendicularly over the object re- 

 presented. Me obtains this end by making the 

 iiiH-s, which represent the declivity of a mountain 

 on a plan, blacker and closer together, if the decli- 

 vity is great, and finer and farther apart, if it is 

 slight. Total white represents a perfect plain ; 

 total black a declivity of 45, as the steepest that 

 can be met with, unless it be a wall of rock, and 

 consequently impassable ; fine widely separated 

 lines indicate a slope of 5; broader and closer 

 lines one of 10; still closer lines one of 15, and 

 so on for every 5, to 45. The whole is founded 

 on mathematical principles, and on the fact, that, 

 to an observer, the declivity in a landscape will 

 appear shaded in proportion to its inclination, while 

 a level plain will appear in the strongest light, 

 without shade. Plans projected in this manner are 

 of the greatest service in the field, because they 

 appear to a practised eye like a perfect picture. 

 It is even possible to draw the profile of a mountain 

 from a plan well executed in Lehmann's manner. 



PROGNE, PROCNE. See Philomela. 



PROGNOSIS; the foretelling the event of 

 diseases from particular symptoms. Those symp- 

 toms which enable the physician to form his judg- 

 ment of the cause or event of a disease are called 

 prognostics. 



PROGRESSION, in arithmetic and algebra ; a 

 series of numbers advancing or proceeding in the 

 same manner, or according to a certain law, &c. 

 Progression is either arithmetical or geometrical. 

 Arithmetical progression is a series of three or more 

 quantities that have all the same common difference; 

 as 3, 5, 7, &c., which have the common difference 

 2. Geometrical progression is a series increasing 

 by a common multiplicator, so that each term con- 

 tains the preceding a certain number of times. 



PROHIBITIVE SYSTEM. See Political Eco- 

 nomy. 



PROJECTILE; a heavy body, which being put 

 in motion by an external force impressed upon it, 

 is dismissed from the agent and left to pursue its 

 course; examples of projectiles are a stone thrown 

 from the hand, a bullet from a gun, &c. The theory 

 of the motion of projectiles is a part of higher me- 

 chanics, and is of great importance in the science 

 of gunnery. Bodies may be projected perpendicu- 

 larly, horizontally, or obliquely, and are acted upon 

 both by the force of projection and the force of 

 gravity; the path which they describe must there- 

 fore depend upon the ratio of these forces. Besides 

 these two elements, a third is presented by the 

 resistance of the medium (as, for instance, the air) 

 through which the projectile is driven. When the 

 direction of the projecting force is perpendicular, 

 the path of the projectile is a right line; if it be 

 downward, the motion is accelerated by the force 

 of gravity; if upward, it is retarded, and finally an- 

 nihilated, and the body then falls by its mere gravity. 

 But in the case of horizontal or oblique projection, 

 when the direction of the projecting force and that 

 of the force of gravity form an angle with each 

 other, the result is a curvilinear motion ; and, ac- 



cording to the laws of falling bodies, discovered by 

 Galileo, the path of the projectile, setting aside the 

 resistance of the air, is a parabola. The principles 

 deduced from the laws of Galileo constitute the 

 theory of the parabolic motion of projectiles, in 

 which they are considered as moving in a non-resist- 

 ing medium. The problem to determine the effect 

 of the resistance of the air is, however, of great 

 practical importance, and was first solved by 'IVm- 

 pelhof in his Bombardier Prussien. See the articles 

 Mechanics, and Parabola. 



PROJECTION, in perspective, denotes the ap- 

 pearance or representation of an object on the per- 

 spective plane. See Perspective. 



PROJECTION OF THE SPHERE IN PLANO 

 is a representation of the several points or places of 

 the surface of the sphere, and of the circles describ- 

 ed upon it, according to the places which their 

 images occupy, upon a transparent plane placed 

 between the eye and the sphere, or such as they 

 appear to the eye placed at a given distance. The 

 principal use of the projection of the sphere is in 

 the construction of planispheres, maps, and charts, 

 which are said to be of this or that projection, ac- 

 cording to the several situations of the eye and the 

 perspective plane, with regard to the meridians, 

 parallels, and other points or places so represented. 

 The most usual projection of maps of the world is 

 that on the plane of the meridian, which exhibits a 

 right sphere, the first meridian being the horizon. 

 The next is that on the plane of the equator, which 

 has the pole in the centre, and the meridians the 

 radii of a circle, &c. The projection of the sphere 

 is usually divided into orthographic and stereogra- 

 phic, to which may be added gnomonical. Ortho- 

 graphic projection is that in which the surface of 

 the sphere is drawn upon a plane cutting it in the 

 middle ; the eye being placed at an infinite distance 

 vertically to one of the hemispheres. Stereographic 

 projection of the sphere is that in which the surface 

 and circles of the sphere are drawn upon the plane 

 of a great circle, the eye being in the pole of that 

 circle. Gnomonical projection of the sphere is that 

 in which the surface of the sphere is drawn upon 

 an external plane commonly touching it, 'the eye 

 being at the centre of the sphere. 



PROLEGOMENA (Greek*); preliminary obser- 

 vations, serving as an introduction to a work, to 

 which they are prefixed, and containing historical, 

 critical, &c. illustrations of its contents, language, 

 form, &c. 



PROLOGUE, in dramatic poetry; an address 

 to the audience, which precedes the piece itself, 

 that is, the proper action. It may be either in 

 prose or verse, and is usually pronounced by one 

 person. Among the ancients, the player who 

 delivered this address was called the prologus, and 

 was usually considered as a person of the drama. 

 Thus in the Amphitryon of Plautus, Mercury ap- 

 pears as prologus. Prologues sometimes relate to 

 the drama itself, and serve to explain to the 

 audience some circumstances of the action, some- 

 times to the situation in which the author or actor 

 stands to the public, and sometimes have no im- 

 mediate connexion with either of these persons or 

 subjects. See Epilogue. 



PROMETHEUS, a Titan, son of Japetus and 

 Clymene, a daughter of Oceanus ; ^Eschylus makes 

 Themis, Apollodorus Asia, his mother. He was 

 the father .of Deucalion. Cunning and fertile in 

 expedients, he opposed Jupiter, the founder of the 

 new race of the gods, whom he had at first sup- 

 ported ; and when some of the Titans proposed to 

 expel Saturn from the throne, and elevate Jupiter 

 in his place, Prometheus advised them to work by 



