269 



PARABOLIC REFLECTOR. 



PARADOX. 



270 



The point 8 is the focus, and the line L M the directrix. The ordinate 

 s K drawn through the focus is called the semi-latus-rcctum, and doubl 

 of it is the latus rectum. The same phrase is used for the ordinate 

 drawn through the focus of an ellipse or hyperbola. 





3. B A la equal to A L, and s K to twice A s. 



4. If an ellipse be described with the vertex A and the focus s, the 

 farther the centre is from the point s, the more nearly will the part of 

 the ellipse which falls within any given ordinate T N coincide with the 

 corresponding part of the parabola : and the same of an hyperbola 

 drawn with the vertex A and focus s. And a parabola may be con- 

 sidered as an ellipse or hyperbola with a given focal distance A s, and a 

 centre at an infinite distance. 



5. The tangent P T bisects the angle M p s, and s P is equal to s T, 

 and AX to AT. The line 8 T drawn perpendicular to the tangent 

 from the focus always meets FT in a point of the tangent drawn 

 through A. 



6. If the normal pa be drawn perpendicular to FT, then s r is equal 

 to 8 o, and x o is always equal to twice A 8. 



7. The square on p x is equal to four times the rectangle under A x 

 and A 8. 



8. The area A K P is two-thirds of X z, the rectangle under A N and N p. 



9. If Q Q' be drawn parallel to FT through any point v of the 

 diameter P v, Q <J Li bisected in V, and the square ou q v is equal to four 

 tunes the rectangle under BP and FT. 



10. The square on a Y U equal to the rectangle under AS and s p. 



In applied mathematics the parabola was formerly of great im- 

 portance, both as being the curve in which a comet was suppoeed to 

 move, and as that in which a cannon-ball or other projectile would 

 move were it not for the resistance of the air. It is still sometimes 

 used as the approximation to the elongated ellipse in which a comet 

 moves. For the more accurate investigations which deduce the real 

 path of a projectile, see Gux s 



PARABOLIC REFLECTOR. It is well known in Coxic SECTIOXS 

 that lines joining the foci and any point of the curve, make equal 

 angles with the tangent at that point ; hence by the law of REFLEXION 

 if the surface of a mirror be formed by the revolution of a conic sec- 

 tion about its axis, a pencil of rays incident upon its surface from 

 either focus will, after reflexion, converge to or diverge from the 

 :>'.! i". Mil row in the form of a parabola are used in reflecting 

 telescopes, and in light-houses; but in the former the incident and in 

 the latter the reflected is the parallel pencil of rays. The conjugate 

 mirrors used for illustrating some of the phenomena of radiant HEAT, 

 are of this kind, and such mirrors are also being introduced for con' 

 ng fog and other signals by means of sound. 



: ABOLOID. The simplest form of this surface is the para- 

 boloid i'f revolution, made by the revolution of a parabola about its 

 axis. For the other meanings of the term, see SURFACES OF TIIK. 

 SECOND DixiRr.K. The solidity of the part of the paraboloid described 

 by the revolution of A p x [PARABOLA] is always half that of the 

 cylinder described by AZPN. 



PARACESTBIC, or " towards the centre," a term sometimes used, 

 as in paracentric velocity, which means the rate at which a moving 

 body approaches a certain centre without reference to the rate at 

 which it moves in space. 



PARACHLOROBENZOIC ACID. [BEszoic ACID.] 



PARACHL'TE, a French word, signifying a means of preventing 

 a fall. The first part of the word, para, is perhaps of Greek origin ; 

 the second part is the French word chute, a fall, which is of Latin 

 origin. 



A parachute is a machine attached to a balloon, and is intended to 

 convey th aeronaut gently to the earth, in case of an accident happen- 



ing to the balloon. It is in shape like an umbrella, and its construction 

 may be understood by supposing the umbrella to be large and strong, 

 to be provided with ropes or stays fastened to the extremities of the 

 whalebones, and brought down to the handle, where they must be 

 fixed, so as to prevent the umbrella from turning inside outwards. 

 Instead of the stick, suppose a metal tube to be fixed in the centre, 

 with a rope passing through it, attached by its upper extremity to the 

 balloon, and by its lower end to a tub or car. This machine is a para- 

 chute : while ascending, it will be like a closed umbrella, but it may at 

 any moment be detached from the balloon by cutting the end of 

 the rope which is tied to the car ; the resistance of the air will then 

 cause it to expand, and will at the same time retard the velocity of 

 descent. 



The idea of using such a machine to break the fall from a high place 

 is not new : it has been frequently experimented with ; has been found 

 utterly useless for any desirable purpose ; and has caused the death of 

 many who have attempted to descend by its means. 



Three formulas have been given for calculating the velocity of 

 descent of a parachute. They are 



28-28 V = 

 d- 



in which w is the weight in pounds avoirdupois ; d, the diameter of the 

 parachute ; v the number of feet fall per second. 



According to the first of these, if a parachute be 50 feet in diameter 

 and weigh 529 IbH., it will fall 1T96 feet in a second ; according to the 

 second, the fall will be 13'01 feet; according to the third, 1517 feet : 

 the truth may lie between. 



In these three cases, the shock felt on landing would be nearly equal 

 to that caused by a leap from heights represented by the following 



three formulas respectively: 10-5 ,; 12-4 !L; 16'9 " ; being, under 



d* d' d* 



the given circumstances, something less than 2 feet 3 inches, 2 feet 

 8 inches, and 3 feet 7 inches : a fall, therefore, of two or three thousand 

 feet would almost certainly be fatal. 



PARACHUTE LIGHT is a description of light-ball invented by 

 Captoin Boxer, R.A. It consists of two tin hemispheres, one of which 

 is filled with light ball composition, and has a lid soldered on to it, and 

 four fuse holes made in the convex part through which the composition 

 burns ; and the other hemisphere contains the calico parachute folded 

 up the calico parachute is attached by wires to the hemisphere con- 

 taining the composition. The whole is placed in a paper-shell contain- 

 ing enough powder to burst it, and is fired from a mortar. The fuse 

 is timed to burst it when at the greatest height. The parachute being 

 then liberated supports the hemisphere containing the composition in 

 the air, which burning out of the fuse-holes throws a strong light on 

 the ground, by which an enemy's working parties and movements 

 during the night may be discovered. 



PARACYANOGEN. When cyanogen is obtained by heating 

 bicyanide of mercury in a retort, there remains in the latter a dark- 

 coloured substance, which was found by Professor Johnston to be 

 similar in composition to cyanogen, that is, composed of 2 equivalents 

 of carbon 12, and 1 equivalent of nitrogen 14 = 26. It appears there- 

 fore that it is a bicarburet of nitrogen, isomeric with cyanogen, but 

 differing from it essentially in its physical and chemical properties, the 

 paracyanogen being solid whilst cyanogen is gaseous. This com- 

 pound is also formed when mercury is kept in an alcoholic solution of 

 cyanogen. 



PARADE is an assemblage of troops for muster, exercise, inspection, 

 to. The word also signifies the ground on which the exercise and 

 drill are performed. 



PARADISE (wapaSturot) is a word of Persian origin, signifying a 

 kind of park or pleasure-ground inclosed with walls, and well watered 

 and planted, and stocked with animals for the chase. (Pollux, ix. 13 ; 

 >llius, ii. 19.) It was adopted into the Greek language, and applied 

 ;o_any pleasant place. The Septuagint translators use this word for 

 7/1J. the garden of Eden, where God placed the first man upon 

 lis creation. (Gen. ii. 8; iii. 23) Respecting the situation of this 

 >lace, we are told, in Gen. ii. 8-14, that it lay eastward in the land of 

 Sden, and that it was watered by a river, which, after passing through 

 the garden, divided into four streams, of which the first, Pison, com- 

 passed the land of Havilah, where there was gold, bdellium (either the 

 >earl or a sort of gum resin), and the onyx stone ; the second, Gihon, 

 compassed the land of Cush; the third was Hiddekel (the Tigris), 

 vhich went towards the east of Assyria; the fourth was the Euphrates. 

 Uany attempts have been made to fix the position, but nothing satis- 

 aotory has been, or can be, ascertained, as it is clear the face of the 

 earth, and probably the course of the streams, must have undergone 

 great changes since the period of its existence. 



PARADOS is a traverse placed in fortifications in the rear of a work, 

 to cover it from reverse fire. 



PAR'ADOX (from irop<Jocr, " contrary to received opinion ") is a 



