PARALLAX is the apparent displacement of an object caused by a change of place in the observer. When an object at M is locked at from P, it appears in line with some object, S; lint after the observer has moved to E. M has apparently retrograded to a position in line with S'; this apparent retro gression is denominated parallax. The angle is called the " angle of parallax," or the "parallactic angle," 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 necessity of referring all observations to the earth's center, i.e. so modifyin them as to make it appear as if they had been actually made at center; and secondly, because parallax is our only means of determining the magnitude and distance of the heavenly bodies. The geocentric or daily parallax as the apparent displacement of a heavenly body, due to its being observed front a point ou the surface of the earth instead of from its center, is called—is determined as follows: Let 1' and P' be two stations on the surface of the earth (fig. 2), E its center, M the object to be observed, and Z and Z' the zeniths respectively of the ohserv. ers at P and P' (points which, if possible, should be on the same meridian exactly); then at P and P' let the zenith distances, ZPM and Z'P'3I, be observed simultaneously, and since the latitudes of P and P', and consequently their difference of latitude, or the angle PEP', is known, from these three the angle (the stun of the laxes at P and P') is at once found; and then, by a trigonometrical process, the separate angles or parallaxes PME and P'3IE. When the parallax of N, as observed from P, is known, its distance front E, the center of the earth, can be at once mund. When the heavenly body is on the horizon, as at 0, its parallax is at a maxi mum, and is known as the horizontal parallax. The geocentric parallax is of use only in determining the distances of those heavenly bodies at which the earth's radius subtends a considerable angle; and as the moon and Mars (when in opposition) are the only such bodies, the parallax of the other celestial bodies must be determined in a different man ner. The parallax of the sun (q.v.) is found by observation of the transit
across his disk, a much more accurate method than that above e :scribed. The paral laxes of the other planets are easily determined from that of Mars.
In the case of the fixed stars, at which the earth's radius sut ends an infinitesimal angle, it becomes necessary to make use of a much larger base-line than the earth's radius, and, as the largest we can employ is the radius of the earth's orbit, it accordingly is mad:: use of, and the displacement of a star, when observed from a point in the earth's orbit instead of from its center, the sun, is called the annual 1r heliocentric parallax. Here the base-line instead, as in the former case, of being,' N:10 1., is about 92,000,000 tn., and the two observations necessary to determine the paraffactic angle are made front two point.3 on opposite sides of the earth's orbit, at an interval as nearly as possible of half a year. Yet, notwithstanding the enormous length of the base-line, it bears so small a proportion to the distances of the stars, that only in three or four cases have they been found to exhibit any parallactic motion whatever, and in no case does the angle of parallax amount to 1" (see STARS). The geocentric horizontal parallax of the moon is about 57' 4.2"; that of the sun, about 8.6"; and of the double star, 61 cygni, the heliocentric parallax has been determined by Bessel to be .348", equivalent to about 15 millionths of a second of geo centric horizontal parallax. Parallax affects every observation of 'angular measurement in the heavens, and all observations must be corrected for parallax,- or in astronomical phrase, referred to the earth's center before they cast be made use of in calculation. The position of a body, when noted from the surface of the earth, is called its apparent posi tion; and when referred to the center, its real position.