7.V- 



PARAOUAY TEA 



PARALLELOGRAM 



J>J*nviy(PrU.1889); Vincent, Around and About 

 SamtA Amenta 



Paraguay Tea. See MAT. 



Parahj lia. capital of the Brazilian state of 

 Parahyhn, on tin- river if tin- same imine, 10 miles 

 from tlie wo. It* chief building- are the cathedral 

 anil the government palace (formerly the Jesuit 

 college). A large sugar-mill was erected in 1S89. 

 At the mouth of the river i a bar; l>ut a railway 

 (12 miles) was luiilt in 1889 to _t he port of Cabe- 

 ilello, there terminating in a pier ii. map water. 

 The annual exports ungar, cotton, and cotton- 

 seed, chiefly to Great Britain amount to about 

 200,000. Pop. 14,000. The thitc, the eastern- 

 most in the ri-pulilic, lias an area of 28,854 sq. 

 m. and a pop. (1890) of 4.17. 232. There is a 

 more important Parahyba River farther south, 

 which enters the Atlantic. in tin- state of lli<> M 

 Janeiro, after a course of nearly .VKl miles. It is 

 navigable for 60 miles from its mouth. 



Parallax is the apparent displacement of an 

 object caused by a change of place in the observer. 

 When an object at M U looked at from P it 



FSg.1. 



appears in line with some object, 8 ; but after the 

 observer has moved to E, M has apparently moved 

 to a position in line with S' ; the amount of appar- 

 ent motion is called jmrallar. The angle PME 

 is called the 'angle of parallax,' or the 'paral- 

 lactic angle, 1 and is the measure of the amount of 

 parallax. To astronomers the determination of the 

 parallax of the heavenly bodies is of the utmost 

 importance, for two reasons first, from the neces- 

 sity of referring all olnervations to the earth's 

 centre i.e. so modifying them as to make it appear 

 as if they had Ijeen* actually mode at the earth's 

 centre ; and secondly, liecause parallax is our only 

 means of determining the magnitude and distance 

 of the heavenly Inxlies. The geocentric or daily 

 parallax as the apparent displacement of a 

 heavenly liody, due to its being observed from a 

 point on the surface of the earth instead of from 

 us centre, is called is determined as follows : Lei 



P and F be two 

 stations on the 

 surface of the 

 earth (fig. 2), E 

 its centre, M tli< 

 object to be ob 

 nerved, and 7 

 and / the zeniths 

 respectively o 

 the observers a 

 P and P' ( point* 

 whirl), if poe 

 sihle, should l> 

 on the name me 

 ridian exactly) 

 then at P and I 

 let the tenilh dittanra, ZPM and Z'PM, In 

 observed simultaneously, and, since the latitude 

 of 1' and 1'', and consequently their difference o 

 latitude, or the angle 1'K.I' ', i* known, from these 

 three the angle P.M P* ( the sum of the parallaxes 

 at P and r) is at once found , and then, by 

 trigonometrical process, the separate angles o 

 parallaxes PMK and I'MF. When the paralla 

 nf M. as observed from P, is known, it* distanc 

 from E, the centre of the earth, can be at once 



nind. When the heavenly Ixidy i on the horizon, 

 s a?. O, it* parallax is at a maximum, and 

 nown as tin- linri::<iitl parallax. The gem-en- 

 arallax i of u-o onlv in determining the distances 

 f those heavenly toold at which the earth's radius 

 iiliK'inIs a considerable angle. 



In the case of the fixed -tars, at which the earth s 

 railius subtends nn infinitesimal angle, it bwMMi 

 ecessary to make Use of a much larger base-line 

 lian the' earth's radius, and, as the largest we can 

 mploy is the radius of the earth's orhit, it accord - 

 ngly is made use of, and the displacement of a 

 tar, when observed from a point in the earth's 

 n-hit instead of from its centre, the sun, U culled 

 he niunnil or htliorcntrir parallax. Here the l>a-e 

 ine, instead of lieing, as in the former case, 4<MH) 

 miles, is about 92,000,000 miles, and the two 

 ih-ervations necessary to determine the parallactic 

 Angle are maile from two points on opposite sides 

 of the earth's orhit, at an interval as nearly as 

 possible of half a year. Yet. notwithstanding the 

 enormous length of the iMVse-line, it bears BO small 

 a proportion to the distances of the stars that only 

 n ft few case* have they lieen found to exhibit any 

 mrallactic motion whatever, and very rarely docs 



he angle of parallax amount to 1" (see STARS). 

 The geocentric horizontal parallax of the moon is 

 about 57' 4-2" ; that of the sun, almut 8'8" ; and of 

 ;he double star, 61 Cyyni, the heliocentric parallax 

 las been determined'by Bessel to be '348", equiva- 

 ent to about 15 millionth* of a second of geocentric 

 lori/ontnl parallax. See the articles STARS and 

 }UN. 



Parallel Forces are forces which act in 

 parallel lines, such for example as the weights of 



he portions that make up any framework or 

 structure on the earth's surface. With the cxcep- 



ion of a particular case (see COUPLE), parallel 

 forces have always a single resultant, which is 

 readily found by the method of moments. See 

 MoMKXT ; also FOBOR 



Parallel Motion, a name given to any link- 

 age by which circular motion may lie changed into 

 straight line motion. The most familiar instance 

 is Watt's parallel motion (see Si i: \M KN>;INK), 

 which is essentially a three -bar linkage, and, 

 although not theoretically perfect, is sufficiently 

 good for all practical purposes. It is impossible, 

 indeed, to obtain a straight line motion without 

 the use of at least /f re bars in the linkage ; and till 

 1*7-1. when Hart discovered the method, even this 

 simplest mode of obtaining a, true parallel motion 

 was not deemed possible. The Peaucellier cell, a 

 linkage of seven bars, was, however, the earliest 

 linkage discovered for solving the problem of how 

 to draw a straight line. It dates from 1864, and 

 is, perhaps, the 

 most convenient 



form that has 



vet been devised. 



It is shown in 



the figure. The 



equal links AT, 



AQ, BP. BQ, 



form a rhomlms; 



the long links 



OA, OB, are also 



ec|iml, and have 



the common 



point <> lixed. The seventh link, QC, has its end C 



lixed. so that Q describes a circle passing through 



O Le. QC equals the lixed distance CO. In these 



circumstances, when Q moves in its circle P moves 



in a straight line. See A. B. Kemp's How to draw 



a Straight Line ( ' Nature ' series, 1877 ). 



Parallelogram of Velocities. See COM- 

 POSITION. 



