PARALLAX PARALOGISM. 



413 



but they were forced to retreat. The inhabitants, 

 however, soon after deposed the governor themselves, 

 and formed a junta, which administered the govern- 

 ment in the name of Ferdinand VII. In 1813, they 

 proclaimed Paraguay a republic under two consuls 

 doctor Francia and Yegros. At the end of the year, 

 the former caused himself to be named dictator for 

 three years, and, at the expiration of that term, for 

 life. In 1826, lie first declared Paraguay indepen- 

 dent, and, in 1827, its independence was formally 

 acknowledged by dom Pedro, then emperor of Brazil. 

 Under the domination of doctor Francia, Paraguay 

 has been reduced to order, and advanced considerably 

 in prosperity, although he has committed many most 

 outrageous acts of tyranny. The celebrated Bon- 

 pland, who received orders to leave the country in 

 1829, was afterwards detained until February, 1831, 

 having been confined nine years. The two travellers 

 Rengger and Longchamps, who were detained in 

 the country six years (1819 1825), have published 

 an Essai sur le Gouvernement dictatorial du Doctor 

 Fru/icia (Paris 1827 ; English, London, 1830). 



The inhabitants are Creoles, who compose about 

 seven tenths of the population ; natives (Guaranas), 

 one tenth; the blacks and mixed breeds, with a few 

 hundred Spaniards, the remainder. The standing 

 army of the dictator consists of 5000 men ; the 

 militia, of 20,000. The climate of Paraguay is mild 

 and healthy, but tnoist ; the face of the country is 

 level, and the soil in general fertile. Tropical fruits, 

 corn, and the vine, thrive very well ; the sugar-cane, 

 rice, maize (of which the natives make an intoxicat- 

 ing drink), excellent tobacco, indigo, various drugs, 

 such as jalap, quinquina, rhubarb, &c., and many 

 valuable forest trees, abound. The matte, or Para- 

 guay tea-plant, is a small plant, the leaves of which 

 resemble senna ; they are dried, and used all over 

 South America, in the form of an infusion, as the tea 

 of China is used with us. The principal articles of 

 export are matte, tobacco, sugar, cotton, wax, and 

 tallow and hides obtained from the immense herds 

 which roam in the vast plains of Paraguay. The 

 ostrich, parrots, boas, rattle-snakes, cougars, and 

 jaguars are among the wild animals. 



PARALLAX ; the angle formed by two different 

 lines of view drawn towards one and the same object. 

 Suppose a point is seen from the two ends of a 

 straight line ; the two lines of view towards that 

 point form, with the other straight line, a triangle 

 whose angle at the object is the parallax. The 

 parallax is of particular importance in astronomy for 

 the calculation of the distance of heavenly bodies. 

 These may be observed from very different points on 

 the globe, and appear accordingly, and according to 

 their distance at different places in the heavens. The 

 astronomer, however, considers himself at the centre 

 of the globe, calculates the place of the heavenly 

 body with reference to this imaginary place of 

 observation, and calls the place thus found the true 

 or mean, in contradistinction to the apparent place, 

 observed from the surface of the globe. If the 

 heavenly body were seen precisely in the horizon, 

 and if we suppose, at the same time, another line of 

 view drawn from the centre of the earth to the same 

 body, these two lines of view would include, with 

 the radius of the globe, a right-angled triangle, in 

 which the angle at the heavenly body would be its 

 horizontal parallax, and the hypothenuse the dis- 

 tance of the star from the centre of the earth. From 

 this horizontal parallax, therefore, we may calculate 

 the distance of the heavenly body according to trigo- 

 nometrical laws. The horizontal parallax, it is true, 

 cannot be observed directly, but the parallax of 

 altitude can be so observed. This expression desig- 

 nates the angle at the star, when elevated above the 



horizon. From the parallax of altitude follows the 

 horizontal parallax, and hence the distance. See 

 Bode's Introduction to Astronomy, 3d edit. (Berlin, 

 1808, vol. i. sect. 542 et seq.) It ought to be 

 added, that this parallax is called the daily, in con- 

 tradistinction to the annual, by which, in general, is 

 understood the difference of the place of a heavenly 

 body as seen from the earth and from the sun ; par- 

 ticularly, however, the angle formed by two lines 

 from the ends of the diameter of the earth's orbit to 

 a fixed star, which angle, on account of the immense 

 distance of the fixed stars, is too small to be ascer- 

 tained. See Fixed Stars. 



PARALLELISM OF THE EARTH'S AXIS is 

 used to denote that invariable position of the terres- 

 trial axis by which it always points to the same point 

 in the heavens, abstracting the trifling effect of nuta- 

 tion, &c. See Nutation. 



PARALLEL LINES, in mathematics; two lin*-> 

 which, continued ad infinitum, never approach, or 

 remain always at the same distance. The theory o 

 parallels is of the highest importance in mathematics, 

 being an essential element of most demonstrations 

 yet, though every thing asserted of them in mathe 

 ma tics is evident, the strict demonstration of the 

 theory has given mathematicians great trouble, and 

 not a few have lost much time, and some even theii 

 reason, in the attempt. In this respect, the theory 

 of parallel lines is somewhat like that of the squaring 

 of the circle. 



Parallel is often used metaphorically, to denote 

 the continued comparison of two objects, particularly 

 in history. Thus we speak of drawing an historical 

 parallel between ages, countries, or men. Plutarch 

 wrote biographical parallels. Parallel passages 

 signifies passages which agree in import ; as, for 

 instance, the parallel passages in the bible. 



Parallelism, in Hebrew poetry, is the correspon- 

 dence of two successive lines in imagery, sense, or 

 grammatical construction. 



Parallel circles, or circles of latitude, are those 

 circles which run parallel to the equator, and become 

 therefore smaller and smaller towards the pole. See 

 Latitude. 



Parallel lines, in sieges, are those trenches which 

 generally run parallel with the outlines of the fortress. 

 They serve as places for concentrating the forces to 

 be directed against the fortress, and are usually three 

 feet deep, from nine to twelve feet wide, and of a 

 length adapted to the circumstances of the case. 

 Generally three parallel lines are requisite before a 

 breach is made, the most distant of which is from 

 600 to 900 paces from the covered way of the for- 

 tress ; and the last receives the apparatus destined 

 to effect the breach, and is made on the glacis itself. 

 The communication from one to the other is effected 

 by means of ditches. Vauban first made use of 

 them in 1763, at the siege of Maestricht- 



PARALLELOGRAM OF FORCES is a term 

 used to denote the composition of forces, or the 

 finding a single force that shall be equivalent to two 

 or more given forces when acting in given direc- 

 tions. 



PARALLELOPIPED, in geometry; a regular 

 solid, comprehended under six sides or parallelo- 

 grams, the opposite ones of which are similar, pjiral- 

 lel, and equal to each other. 



PARALLEL SAILING, in navigation, is the 

 sailing under a parallel of latitude. See Navigation. 



PARALOGISM, in logic ; a false reasoning, or a 

 fault committed in demonstration, when a conse- 

 quence is drawn from principles that are false, or, 

 though true, are not proved ; or when a proposition 

 is passed over that should have been proved by tho 

 way. 



