Part 4

I. General Aspect of the Heavens 322

II. The Stars 330

The Constellations 330

Clusters 350

Double and Multiple Stars 355

New and Variable Stars 358

Distance of the Stars 364

Proper Motion of the Stars 365

Chemical and Physical Constitution of the Stars 371

III. Nebulæ 373

Classification of Nebulæ 373

Irregular Nebulæ 376

Spiral Nebulæ 384

The Nebular Hypothesis 391

IV. The Structure of the Stellar Universe 396

I. THE CELESTIAL SPHERE.

I. The Sphere.--A sphere is a solid figure bounded by a surface which curves equally in all directions at every point. The rate at which the surface curves is called the curvature of the sphere. The smaller the sphere, the greater is its curvature. Every point on the surface of a sphere is equally distant from a point within, called the centre of the sphere. The circumference of a sphere is the distance around its centre. The diameter of a sphere is the distance through its centre. The radius of a sphere is the distance from the surface to the centre. The surfaces of two spheres are to each other as the squares of their radii or diameters; and the volumes of two spheres are to each other as the cubes of their radii or diameters.

Distances on the surface of a sphere are usually denoted in degrees. A degree is 1/360 of the circumference of the sphere. The larger a sphere, the longer are the degrees on it.

A curve described about any point on the surface of a sphere, with a radius of uniform length, will be a circle. As the radius of a circle described on a sphere is a curved line, its length is usually denoted in degrees. The circle described on the surface of a sphere increases with the length of the radius, until the radius becomes 90°, in which case the circle is the largest that can possibly be described on the sphere. The largest circles that can be described on the surface of a sphere are called great circles, and all other circles small circles.

Any number of great circles may be described on the surface of a sphere, since any point on the sphere may be used for the centre of the circle. The plane of every great circle passes through the centre of the sphere, while the planes of all the small circles pass through the sphere away from the centre. All great circles on the same sphere are of the same size, while the small circles differ in size according to the distance of their planes from the centre of the sphere. The farther the plane of a circle is from the centre of the sphere, the smaller is the circle.

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.

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.

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.

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.

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.

The sensible horizon is a plane tangent to the earth at the point of observation. The rational horizon is a plane parallel with the sensible horizon, and passing through the centre of the earth. As it cuts the celestial sphere through the centre, it forms a great circle. SN (Fig. 6) represents the sensible horizon, and S'N' the rational horizon. Although these two horizons are really four thousand miles apart, they appear to meet at the distance of the celestial sphere; a line four thousand miles long at the distance of the celestial sphere becoming a mere point, far too small to be detected with the most powerful telescope.