PARALLAX (rapiAAatis), used in astronomy generally for the angular variation in the position of an object caused by the excentric situation of the observer with respect to a certain point of reference. Thus the parallax of the moon, sun, planets, comets, is the difference between the position of any of those bodies as seen from the surface of the earth and that in which they would be seen if the observer were placed at the earth's centre. The parallax of the fixed stars is the difference between their places as seen from the earth and from the sun, which is for these observations the point of reference. All bodies within the solar system are in the first instance referred to the earth's I centre; while those beyond our system, as the fixed stars, are referred to the centre of the sun, and the change arising from excentric position in each case is called parallax.
From the effects of parallax we derive all our knowledge of the distance and magnitude of the bodies which are visible in the heavens.
Let A B be any line the length of which is accurately measured, and let the angles c A B, c B A, be observed, then the distances c A and c can be computed. In this way trigonometrical surveys are made, with the further precaution that the angle A CB is observed when this is possible, and c is to be fixed with great nicety. The angle A C B is known, since it = 180°— (e A c+ An c), and we have A : sin A o B : sin Ca B. In the above figure, let A be the position of a spec
tator on the earth's surface, B the centre of the earth, o the moon, and z (in B A produced) the geocentric zenith. Then z A C is the apparent geocentric zenith distance at A; ziic the true geocentric zenith dis tance, that is, that which would be seen from the centre of the earth; and A c B= zee—zit c, the moon's parallax : also sin parallax = A B x sin Appt. geocent. zen. dist.
BC When A C is at right angles to B A, this sine = 1, and the moon is in the horizon. This value of the parallax is called the horizontal parallax; naming this r, and any other value of the parallax p, we have sin r = and 73 C sin p = sin r x sin appt. geocent. zen. dist.
It is evident that if r can be measured, the distance II of the moon's centre from the centre of the earth can be found, for the other quan tity A 13 or r is the radius of the earth at the place of observation, which is known from terrestrial measurement. Now, suppose a second spectator on the same meridian at A', whose geocentric zenith is z', and that the two observers each observe the moon upon the meridian at the same moment : then, if a and z be two observed geocentric zenith distances, and p and p the = and