PAR 



PAR 



whereby a letter or syllable is added to 

 the end of a word ; as med, forme-, dicier, 

 for did, &c. 



PARALLACTIC, in general, something- 

 relating to the parallax of heavenly bodies. 

 See PAKALLAX. 



The parallactic angle, of a star, &c. is 

 the difference of the angles C E A (Plate 

 Parabola, &c. fig. 11) B T A, under 

 which its true and apparent distance 

 from the zenith is seen ; or, which is 

 the same thing 1 , it is the angle T S E. 

 The sines of the parallactic angle A L 

 T, AST, (fig. 12.) at the same or 

 equal distances, Z S, from the zenith, 

 are in the reciprocal ratio of the distan- 

 ces T L, and 1' S, from the centre of the 

 earth. 



PARALLAX, in astronomy, denotes a 

 change of the apparent place of any hea- 

 venly body, caused by being seen from 

 different points of view ; or it is the dif- 

 ference between the true and apparent 

 distance of any heavenly body from the 

 zenith. Thus let A B (Plate XII. Mis- 

 cell, fig. 1.) be a quadrant of a great cir- 

 cle on the earth's surface, A, the place 

 of the spectator, and the point V, in the 

 heavens, the vertex and zenith. Let 

 V N H represent the starry firmament, 

 A D the sensible horizon, in which sup- 

 pose the star C to be seen, whose dis- 

 tance from the centre of the earth is T 

 C. If this star were observed from the 

 centre T, it would appear in the firma- 

 ment in E, and elevated above the hori- 

 zon by the arch D E ; this point E is call- 

 ed the true place of the phenomenon or 

 star. But an observer viewing it from 

 the surface of the earth at A, will see it 

 at D, which is called its visible or appa- 

 rent place ; and the arch D E, the dis- 

 tance between the true and visible 

 place, is what astronomers call the 

 parallax of the star, or other pheno- 

 menon. 



If the star rise higher above the hori- 

 zon to M, its true place visible from the 

 centre is P, and its apparent place N ; 

 whence its parallax will be the arch 

 P N, which is less than the arch D E. 

 The horizontal parallax, therefore, is the 

 greatest ; and the higher a star rises, the 

 less is its parallax ; and if it should come 

 to the vertex or zenith, it would have no 

 parallax at all ; for when it is in Q, it is 

 seen both from T and T and A in the 

 same line T A V, and there is no differ- 

 ence between its true and apparent or 

 visible place. Again, the further a star is 

 distant from the earth, so much the less 



VOL. Y. 



is its parallax ; thus the parallax of the 

 star F is only G D, which is less than 

 D E, the parallax of C. Hence it is plain, 

 that the parallax is the difference of the 

 distances of a star from the zenith, when 

 seen from the centre and from the sur- 

 face of the earth ; for the true distance 

 of the star M from the zenith is the arch 

 V P, and its apparent distance V N, the 

 difference between which, P N, is the 

 parallax. 



These distances are measured by the 

 angles -V T M, and V A M, but V A M 

 V T M = T M A. For the external an- 

 gle V A M = angle A T M -f- angle 

 A M T, the two inward and opposite 

 angles ; so that A M T measures the pa- 

 rallax, and upon that account is itself 

 frequently called the parallax ; and this 

 is always the angle under which the semi- 

 diameter of the earth, A T, appears to 

 an eye placed in the star ; and therefore, 

 where the semi-diameter is seen direct- 

 ly, there the parallax is greatest, viz. in 

 the horizon. When the star rises high- 

 er, the sine of the parallax is always to 

 the sine of the star's distance from the 

 zenith, as the semi-diameter of the earth 

 to the distance of- the star from the 

 earth's centre ; hence if the parallax of a 

 star be known at any one distance from 

 the zenith, we can find its parallax at any 

 other distauce. 



If we have the distance of a star from 

 the earth, we can easily find its parallax ; 

 for on the triangle T A C, rectangular at 

 A, having the semi-diameter of the earth, 

 and T C the distance of the star, the 

 angle ACT, which is the horizontal 

 parallax, is found by trigonometry ; and, 

 on the other hand, if we have this paral- 

 lax, we can find the distance of the star ; 

 since in the same triangle, having AT, and 

 the angle ACT, the distance TC may be 

 easily found. 



Astronomers, therefore, have invented 

 several methods for finding the paral- 

 laxes of stars, in order thereby to dis- 

 cover their distances from the earth. 

 However, the fixed stars are so remote 

 as to have no sensible parallax ; and even 

 the sun, and all the primary planets, ex- 

 cept Mars and Venus when in perigee, 

 are at so great distances from the earth, 

 that their parallax is too small to be ob- 

 served. In the moon, indeed, the paral- 

 lax is found to be very considerable, 

 which in the horizon amounts to a de- 

 gree or more, and may be found thus : in 

 an eclipse of the moon, observe when 

 both its horns are in the same verticaj 





