Fig. 17.
The arc M N is called the parallactic arc, and the angle A C B, the parallactic angle.
It is plain, from the figure, that near objects are much more affected by parallax than distant ones. Thus, the body C, Fig. 17, makes a much greater parallax than the more distant body D,—the former being measured by the arc M N, and the latter by the arc O P. We may easily imagine bodies to be so distant, that they would appear projected at very nearly the same point of the heavens, when viewed from places very remote from each other. Indeed, the fixed stars, as we shall see more fully hereafter, are so distant, that spectators, a hundred millions of miles apart, see each star in one and the same place in the heavens.
Fig. 18.
It is by means of parallax, that astronomers find the distances and magnitudes of the heavenly bodies. In order fully to understand this subject, one requires to know something of trigonometry, which science enables us to find certain unknown parts of a triangle from certain other parts which are known. Although you may not be acquainted with the principles of trigonometry, yet you will readily understand, from your knowledge of arithmetic, that from certain things given in a problem others may be found. Every triangle has of course three sides and three angles; and, if we know two of the angles and one of the sides, we can find all the other parts, namely, the remaining angle and the two unknown sides. Thus, in the triangle A B C, Fig. 18, if we know the length of the side A B, and how many degrees each of the angles A B C and B C A contains, we can find the length of the side B C, or of the side A C, and the remaining angle at A. Now, let us apply these principles to the measurements of some of the heavenly bodies.
Fig. 19.
In Fig. 19, let A represent the earth, C H the horizon, and H Z a quadrant of a great circle of the heavens, extending from the horizon to the zenith; and let E, F, G, O, be successive positions of the moon, at different elevations, from the horizon to the meridian. Now, a spectator on the surface of the earth, at A, would refer the moon, when at E, to h, on the face of the sky, whereas, if seen from the centre of the earth, it would appear at H. So, when the moon was at F, a spectator at A would see it at p, while, if seen from the centre, it would have appeared at P. The parallactic arcs, H h, P p, R r, grow continually smaller and smaller, as a body is situated higher above the horizon; and when the body is in the zenith, then the parallax vanishes altogether, for at O the moon would be seen at Z, whether viewed from A or C.
Since, then, a heavenly body is liable to be referred to different points on the celestial vault, when seen from different parts of the earth, and thus some confusion be occasioned in the determination of points on the celestial sphere, astronomers have agreed to consider the true place of a celestial object to be that where it would appear, if seen from the centre of the earth; and the doctrine of parallax teaches how to reduce observations made at any place on the surface of the earth, to such as they would be, if made from the centre.