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 11 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 1' 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 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 pirallax 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• epee between its true and apparent or visible place. Again, the further a star is distant frem the earth, so much the less 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 These distances are measured by the angles T M, and V A M, but V A M — VTM=TM A. For the external an gle V A M= angle A '1' M 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 distance.
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 A C T, 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 en eclipse of the moon, observe when both its horns are in the same vertical circle, and at that instant take the alti tudes of both horns : the difference of these two altitudes being halved and add ed to the least, or subtracted from the greatest, gives nearly the visible or appa rent altitude of the moon's centre ; and the true altitude is nearly equal to the al titude of the centre of the shadow at that time. Now we know the altitude of the shadow, because we know the place of the sun in the ecliptic, and its depression under the horizon, which is equal to the altitude of the opposite point of the eclip tic in which is the centre of the sha dow. And therefore, having both the true altitude of the moon and the ap parent altitude, the difference of these is the parallax required. But as the pa rallax of the moon increases as she ap proaches towards the earth, or the peri gxum of her orbit, therefore astrono mers have made tables, which shew the horizontal parallax for every degree of its anomaly.
The parallax always diminishes the al titude of a phenomenon, or makes it ap pear lower than it would do, if viewed from the centre of the earth ; and this change of the altitude may, according to the different situation of the ecliptic and equator in respect of the horizon of the spectator, cause a change of the latitude, longitude, declination, and right ascen sion of any phenomenon, which is called their parallax. The parallax, therefore, increases the right and oblique ascension ; diminishes the descension ; diminishes the northern declination and latitude in the eastern part, and increases them in the western ; but increases the southern both in the eastern and western part ; dimi nishes the longitude in the western part, and increases it in the eastern. Hence it appears, that the parallax has just op posite effects to refraction. See REFRAC