PAR'ALLAX (from Gk. :rctoCANcl..i(s. parai laxis. alternation. from 77-apaX \ a,r,reo, parallaA sein, to make alternate, from Tapd, para. beside dA.NriTc-ecv, allfmsrin. to alter, from d‘Nos. other). The apparent di-placement of an object caused by a change of place of the observer. When an object at M (Fig. 1) is locked at from P, it appears in line with some other object. but after the observer ha- moved to E, Al has ap parently retrograded to a position in line with : this apparent retrogression is called parallax. The angle PALE is called the angle of parallax. and is the measure of the amount of parallax. To astronomers the determination of the parallax of the heavenly bodies is of the greatest impor tance. for two reasons—tirst. from the necessity of referring all to the earth's cen tre. i.e. so modifying them as to make it appear as if they had been actually made at the earth's centre; and secondly. because parallax is our only means of determining the magnitude and distance of the heavenly bodies. The geocentric parallax. the apparent displacement of a heaven ly body due to it- being observed from a point on the surface of the earth instead of from its centre, may be determined as follows: Let P and P' be two stations on the surface of the earth (Fig. 2), E its centre, 31 the object to be ob served, and Z and Z' the zeniths respectively of the observers at P and P', then at P and P' let the zenith distances. ZP51 and Z'P'31. be observed simultaneously, and since the latitude- of P and and consequently the angle PEP'. is known. from these three the angle PIP' (the sum of the parallaxes at P and P') is at once found: and then by trigonometry the separate angles or parallaxes PME and P'51E. When the parallax of M. as observed from P. is known. its distance from E. the centre of the 'arth. can he at once found in terms of the earth', radius as a unit. When the heavenly body is on the horizon. as at 0. its geocentric parallax i maximum. and is known as the hori:ontal paral lax.
In the case of the fixed stars which are so far away that to them the earth's radius sub tends only 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 made use of. and the displacement of a star. when observed from a point in the earth's orbit instead of from its centre. the -um is called the annual or he/foe-tarn' parallax. Here the base-line. instead, as in the former case, of being 4000 miles. is about 9e..•.410.(l00 n ilex. and the two observation= necessary to determine the parallactic angle are made from two point on opposite sides of the earth's orbit, at an in terval 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 dis tance- of the stars that only in a few cases have they been found to exhibit any parallactic motion whatever, and in no case doe- the angle of paral lax amount to I". See 'TAR.
:SOL-kR PARALLAX. The extremely precise de termination of this quantity is very important.
since the solar parallax i- our only mean- of determining the distance of the sun from the earth. This is the fundamental unit of distance in astronomy. Upon it depend directly all our notions as to the magnitude and distance of the other members of the solar system. and ci the universe in general. The solar parallax problem is not only the most important one in fundamental astronomy. but it is alSo. perhaps. the one offer ing the greatest difficulty in solution. Agro nomical instruments enable us to submit to actual measurement only the direction- in -pace of the heavenly bodies. never their distances. These latter must be obtained by computation from measured directions or angles. and for this purpose ;some base-line is indispensable. The largest possible terrestrial ba=e-line is of course a diameter of the earth. Yet so small is even this compared with the distance of the gin, that it would subtend an angle of only about eighteen second, of are to an imaginary observer at the sun's centre. When we reflect that an angle of one second corresponds to only three-tenth= of an inch at a distance of one mile. we get some idea of the extreme minuteness of the earth', diameter as seen from the It i= never possible. of course. to get a complete diameter of the earth for a base-line; but ex traordinary effort- have been made to come as near as py.,ible to this ideal condition. For many years observations of transits of Venus were considered the most favorable mean- of measuring the small angular differences of direc tion of the sun's centre a- seen from opposite side= of the earth. No expense was =pared. espe cially for the transit= of 74 and to secure very complete observations. Yet. altIn ugh the various civilized government- of the world sent out numerous and most elaborately equipped ob serving expedition-, the whole operation turned out practically a failure. It was -imply imp. s sible by this method to secure observation- of the requisite precision. Of late year=. two ether method= have been pretty generally agreed upon a= the he-t. The first is based up. n the so-called constant of the aberration of light. ('-ce ABER RATION OF LIGHT). It is km wn that the directions in which we See the -tar- are appar ently thrown forward toward that print 01 ti e sky to which the orbital motion of t' e earth is carryinr• the observer. It i- a ien. n to the well-known fact that if a n-an be running in a rain-storm the falling drop- to slant toward him though they may really be falling vertically. So their direction seem= t) be thrown forward in the direction of the observer's n. In the case of the earth's orbital motion around the sun. the observer will be moving in epposite direction, in space at interval- of half a year. Consequently the effect of aberration is reversed. and the so-called 'constant' or amount of aberration admit, of determination from the differences of observation, made -ix months apart. The solar parallax can be com puted from the aberration constant. since we know, with quite sufficient prevision, the velocity of the transmission of light in -pace.