In our childhood, we all probably adopt the notion that the sky is a real dome of definite surface, in which the heavenly bodies are fixed. When any objects are beyond a certain distance from the eye, we lose all power of distinguishing, by our sight alone, between different distances, and cannot tell whether a given object is one million or a thousand millions of miles off. Although the bodies seen in the sky are in fact at distances extremely various,--some, as the clouds, only a few miles off; others, as the moon, but a few thousand miles; and others, as the fixed stars, innumerable millions of miles from us,--yet, as our eye cannot distinguish these different distances, we acquire the habit of referring all objects beyond a moderate height to one and the same surface, namely, an imaginary spherical surface, denominated the celestial vault. Thus, the various objects represented in the diagram on next page, though differing very much in shape and diameter, would all be _projected_ upon the sky alike, and compose a part, indeed, of the imaginary vault itself. The place which each object occupies is determined by lines drawn from the eye of the spectator through the extremities of the body, to meet the imaginary concave sphere. Thus, to a spectator at O, Fig 16, the several lines A B, C D, and E F, would all be projected into arches on the face of the sky, and be seen as parts of the sky itself, as represented by the lines A´ B´, C´ D´, and E´ F´. And were a body actually to move in the several directions indicated by these lines, they would appear to the spectator to describe portions of the celestial vault. Thus, even when moving through the crooked line, from _a_ to _b_, a body would appear to be moving along the face of the sky, and of course in a regular curve line, from _c_ to _d_. [Illustration Fig. 16.] But, although all objects, beyond a certain moderate height, are projected on the imaginary surface of the sky, yet different spectators will project the same object on _different parts_ of the sky. Thus, a spectator at A, Fig. 17, would see a body, C, at M, while a spectator at B would see the same body at N. This change of place in a body, as seen from different points, is called parallax, which is thus defined: _parallax is the apparent change of place which bodies undergo by being viewed from different points_. [Illustration Fig. 17.] The arc M N is called the _parallactic arc_, and the angle A C B, the _parallactic angle_.