By a _section_ of a sphere we usually mean the figure of the surface formed by the cutting; by a _plane section_ we mean one whose surface is plane. Every plane section of a sphere is a circle. When the section passes through the centre of the sphere, it is a great circle; in every other case the section is a small circle. Thus, _AN_ and _SB_ (Fig. 1) are small circles, and _MM'_ and _SN_ are large circles. [Illustration: Fig. 1.] In a diagram representing a sphere in section, all the circles whose planes cut the section are represented by straight lines. Thus, in Fig. 2, we have a diagram representing in section the sphere of Fig. 1. The straight lines _AN_, _SB_, _MM'_, and _SN_, represent the corresponding circles of Fig. 1. The _axis_ of a sphere is the diameter on which it rotates. The _poles_ of a sphere are the ends of its axis. Thus, supposing the spheres of Figs. 1 and 2 to rotate on the diameter _PP'_, this line would be called the axis of the sphere, and the points _P_ and _P'_ the poles of the sphere. A great circle, MM', situated half way between the poles of a sphere, is called the _equator_ of the sphere. Every great circle of a sphere has two poles. These are the two points on the surface of the sphere which lie 90° away from the circle. The poles of a sphere are the poles of its equator. [Illustration: Fig. 2.] 2. _The Celestial Sphere._--The heavens appear to have the form of a sphere, whose centre is at the eye of the observer; and all the stars seem to lie on the surface of this sphere. This form of the heavens is a mere matter of perspective. The stars are really at very unequal distances from us; but they are all seen projected upon the celestial sphere in the direction in which they happen to lie. Thus, suppose an observer situated at _C_ (Fig. 3), stars situated at _a_, _b_, _d_, _e_, _f_, and _g_, would be projected upon the sphere at _A_, _B_, _D_, _E_, _F_, and _G_, and would appear to lie on the surface of the heavens. [Illustration: Fig. 3.] 3. _The Horizon._--Only half of the celestial sphere is visible at a time. The plane that separates the visible from the invisible portion is called the _horizon_. This plane is tangent to the earth at the point of observation, and extends indefinitely into space in every direction. In Fig. 4, _E_ represents the earth, _O_ the point of observation, and _SN_ the horizon. The points on the celestial sphere directly above and below the observer are the poles of the horizon. They are called respectively the _zenith_ and the _nadir_. No two observers in different parts of the earth have the same horizon; and as a person moves over the earth he carries his horizon with him. [Illustration: Fig. 4.] The dome of the heavens appears to rest on the earth, as shown in Fig. 5. This is because distant objects on the earth appear projected against the heavens in the direction of the horizon. [Illustration: Fig. 5.]