All of the stars are in motion, some of them with exceedingly high velocities, but though there are several instances of streams of stars, the members of which are moving along parallel paths with the same velocities, in nearly all cases the stars are found to be moving indif ferently in any direction and with different velocities. Though we do not doubt that their motion is fully determined by the combined pull upon them of all of the bodies which com pose our universe, the nature of the resulting motion in any particular case is necessarily very complicated. Attempts have been made from a study of the actual motions observed to estimate the total mass of our universe and so to form an estimate of the mass of the dark suns and other opaque matter which is invisible to us. But the result is naturally subject to very great uncertainty. It will require the ob servations of many centuries, and perhaps of many millenniums, before the total mass of matter in our universe and its distribution can be determined in this way.
The three fundamental facts which deter mine the great phenomena of astronomy, as we observe them in the course of our lives, are (1) the globular form of the earth on which we dwell; (2) its diurnal rotation on its axis; (3) its annual revolution round the sun. The first of these facts is so familiar to all that we need not discuss it. Out of it grow the general phenomena of the sky. The heavenly bodies surround us in every direction. They are really as numerous by day as by night, only in the former case they are blotted out by the brightness of the sky. To imagine the heavens as they really are we must fancy stars as al ways visible in every part of the sky. Then, by day, we should see the sun among the stars, and perhaps the moon also. Mere observation of a heavenly body gives us no idea of its dis tance. By looking at a star we cannot tell whether its distance is to be measured by hun dreds of miles, by millions or by thousands of millions, which it actually is. Hence, all the heavenly bodies appear to us to be at the same distance, as if they were set upon the interior surface of a stupendous sphere in the centre of which we seem to be placed. This imaginary form is called the celestial sphere; it is one of the most ancient conceptions of astronomy, and it is used in the science to the present day to represent the appearance of the heavens. It is divided into two hemi spheres, a visible and an invisible one. The visible hemisphere is the half which is above the horizon, which we call the sky and can always see, except so far as obstructions or inequalities of the ground may prevent. The
other half is below the horizon, and is hidden from our view because the earth is opaque.
Were the latter transparent, we should see the heavenly bodies in every possible direction. The rotation of the earth on its axis pro duces the phenomena of day and night, and the apparent rising and setting of the heavenly bodies. This is known as the diurnal motion. The latter may be considered in two aspects, either as the real rotation of the earth on its axis, in a direction always toward the east, or as an apparent rotation of the heavens in the opposite direction, due to our being uncon scious of the motion of the earth. In conse quence of the diurnal motion the celestial sphere, seeming to our eyes to carry the heav enly bodies on its interior surface, appears to us to make a daily rotation on its axis. The two opposite points of the celestial sphere situated on the prolongation of the earth's axis are called the celestial poles. On these poles as pivots the celestial sphere seems to turn. They are called north or south ac cording to the direction. Their apparent po sition in the sky depends on the latitude of the place where the observer is situated. A heavenly body situated at either pole does not seem to have any diurnal motion. This is nearly the case with the pole star, which dwell ers north of the equator can always see at an altitude above the northern horizon equal to their latitude. A voyager into the southern hemisphere sees the pole star set when be crosses the equator. Then, the south polar star would be visible if there were one. But it happens there is no bright star very near the southern prolongation of the axis. In the United States, say from 30° to 45° of latitude, the pole star is at a corresponding altitude above the horizon, and all the stars in its neigh borhood appear to make a diurnal rotation round it, without changing their form or posi tion, and without ever setting. Any one who chooses can verify this fact by noting the ap pearance of the northern sky about the end of twilight, and then looking at it again two or three hours later. He will then see that stars below the pole have moved toward the east; those on the east side of it have risen higher, and those on the west side are lower, while those above have moved over toward the west. For us, therefore, the sphere of the heavens may be divided into three parts; a circle round the north celestial pole within which stars never set; a corresponding circle round the south pole, the stars in which never rise above our horizon, and a broad middle region where they rise and set.