Wherever we are situated on the earth, we appear to be in the centre of a vast sphere, on the concave surface of which all celestial objects are inscribed. If we take any two points on the surface of the sphere, as two stars, for example, and imagine straight lines to be drawn to them from the eye, the angle included between these lines will be measured by the arc of the sky contained between the two points. Thus, if D B H, Fig. 3, page 30, represents the concave surface of the sphere, A, B, two points on it, as two stars, and C A, C B, straight lines drawn from the spectator to those points, then the angular distance between them is measured by the arc A B, or the angle A C B. But this angle may be measured on a much smaller circle, having the same centre, as G F K, since the arc E F will have the same number of degrees as the arc A B. The simplest mode of taking an angle between two stars is by means of an arm opening at a joint like the blade of a penknife, the end of the arm moving like C E upon the graduated circle K F G. In fact, an instrument constructed on this principle, resembling a carpenter's rule with a folding joint, with a semicircle attached, constituted the first rude apparatus for measuring the angular distance between two points on the celestial sphere. Thus the sun's elevation above the horizon might be ascertained, by placing one arm of the rule on a level with the horizon, and bringing the edge of the other into a line with the sun's centre. [Illustration Fig. 3.] The common surveyor's compass affords a simple example of angular measurement. Here, the needle lies in a north and south line, while the circular rim of the compass, when the instrument is level, corresponds to the horizon. Hence the compass shows the azimuth of an object, or how many degrees it lies east or west of the meridian.