PARALLAX

(Yunanca köken — orijinale bakınız.) A change PARALLAX. of place or of aspect. The term is used in astronomr to denote the difference between the apparent place of a celestial object and its trv£ place, or that in which it would be seen if the observer were placed at the centre to which the motion is referred. When the point of reference is the centre of the earth, the change of aspect is called the diurnal parallax; when it is the centre of the earth's orbit, the change is called the annual parallax. Diurnal Parallax.— IjQt C be the centre of the earth, A the place of the observer, Z his zenith, and S a celestial body. On observing the body from A, it will be seen in the direction A S, making the angle Z A S with the zenith. But if the observer could be placed at C, he would see the body in the direction C S, making the angle Z C S with the zenith. The difference between these two angles Z A S and Z C S is the parallax of S, which, therefore, is equal to the angle A S C. Hence it appears that the parallax of a celestial body is the angle comprised between two lines drawn from the body, the one to the centre of the earth, and the other to a point on its surface. On account of the immense distance of the fixed stars, the diurnal parallax is altogether insensible with regard to them. It may amount to a degree in respect of the moon; but the greatest parallax of the nearest planet does not exceed 30". It is evident, from the inspection of the figure, that although the distance of the object S remain the same, the angle A S C is not a constant quantity, but is greatest when S is seen in the direction of the horizon A H, and diminishes as the altitude of S increases, until it vanishes altogether at the zenith, where the two lines A S and C S merge into the line C Z. In order to discover the law of this variation, let a = C A, the semidiameter of the earth; di= C S, the distance of the observed object from the centre; Z = Z A S, the apparent zenith distance; and P = A S C, the parallax. Now, the sides of a triangle being in the same proportion as the sines of their opposite angles, we have d: a:: sin. Z: sin. P, whence sin. P =- sin. Z. But as P is always a very small angle, the arc may be substituted for the sine without sensible say, the parallax is proportional to the sine of the zenith distance. At the horizon Z is a right angle, and sin. Z = 1: in thiy case, therefore, the expre ion for the parallax becomes P = y' This is called the horizontal parallax; and when its amount has been determined by any means with respect to a celestial body, the parallax of the body at any altitude is found by multiplying the horizontal parallax by the cosine of the altitude, or sine of the zenith distance. Since the parallax of a body is given in terms of its distance and the earth's semidiameter, it follows, reciprocally, that the distance of the body is given in terms of its parallax. The determination of the parallaxes of the different bodies of the solar system is therefore a problem of great importance in astronomy; but it is attended with considerable difficulty in practice, although the principle on which it depends is extremely simple. It may be described as follows: — Let two observers be stationed at the points O and O', of which the latitudes are supposed to be known, and which are both situated on the same meridian, and let them simultaneously observe the zenith distances of the body M (suppose the moon). These observations will give the angles Z O M and Z' O' M, and, consequently, MOCandMOC. The angle O C O' is also known, being the difference or the sum of their latitudes, according as they are on the same or opposite sides of the equator. But the two sides C O and C O' of the quadrilateral M O C O', being radii of the earth, are also supposed to be known; hence the quadrilateral is determined, and its diagonal C M may easily be computed by the rules of plane trigonometry. But when C M is found, the horizontal parallax is also determined, being equal, by what has been already shown, to the quotient obtained by dividing the radius C O by the distance C M. In this manner the horizontal parallax of the moon was determined by Lacaille and Lalande; the former observing at the Cape of Good Hope, ana the latter simultaneously at Berlin. There are methods, however, 3 L 3 [s. 898]