will be found, moreover, supposing the observer to be situated anywhere in the northern hemisphere, that the more towards the north a star rises, the longer it continues visible above the horizon, and that for a certain region of the northern heavens the stars never set at all, but wheel permanently about a fixed point in the celestial sphere.

Another fact of capital importance connected with the phenomena of the stellar heavens is this, the stars constantly maintain the same position relatively to each other. Thus, if we consider any group of stars-for instance, the well-known group termed the Great Bear-we shall find that, although the stars composing the group vary in position with respect to the horizon when viewed at different times, they always preserve the same mutual configuration. It is for this reason that the general host of the luminaries of the stellar heavens have been denominated Fixed Stars, in contradistinction to another class of bodies to be presently referred to, the positions of which in the celestial sphere are continually varying.

The phenomena which we have just described may be accounted for by supposing the stars to be projected on the concave surface of a sphere which revolves uniformly from east to west upon a fixed axis in twenty-four hours. The point around which the stars in the northern heavens revolve is one of the extremities of this axis. In the southern hemisphere an analogous point in the heavens is visible round which the stars perpetually revolve above the horizon. This is the other extremity of the axis of the sphere.

A few of the luminaries of the stellar sphere are found not to conform to the foregoing general description. If we fix our attention on certain of the brighter stars, they will be seen to be continually changing their positions with respect to the other stars. At one time they are seen travelling from west to east, or in the direction contrary to that of the diurnal motion of the sphere. At other times they appear to travel in the opposite direction, or from east to On the whole, however, their eastward motion exceeds their westward motion, and the result is that they ultimately make the complete tour of the heavens in the direction opposite to that of the diurnal motion of the sphere; then they recommence their courses anew, and pursue the same cycle of changes as before. Bodies of this class are termed planets, the appellation being derived from a Greek word which signifies to wander. The time of completing the tour of the heavens is found to be different for each planet.

Observation shows that the sun and moon also have a motion among the stars, in virtue of which they accomplish the circuit of the celestial sphere, the former in a year, the latter in somewhat more than twenty-seven days. We shall hereafter give more precise details on this head.

Before proceeding to give some description of the general theories which have been propounded with the view of accounting for the various phenomena of the heavens, it will be desirable to consider briefly the shape of the body from the surface of which our observations are made.

Various circumstances concur in proving that the earth is a body of a round or globular figure. Thus, let us consider the case, so frequently cited, of the appearance presented by a ship proceeding out to sea. The different parts of the vessel do not all fade simultaneously into indistinctness from mere distance. On the contrary, the hull of the vessel first disappears, then the lower parts of the rigging, and finally the top of the masts. Now this is exactly the succession of appearances which would be presented if the earth was a round or spherical body.

Again, it is well known that lunar eclipses are occasioned by the moon entering into the shadow which the earth forms by its interception of the sun's rays. Now it has been observed that in all such phenomena the outline of the shadow is circular. This result;

however, can only be explained by the supposition of the earth being a body having the shape of a sphere. Indeed, the figure of the earth is indicated so palpably by observations, even of the most rudimentary kind, that it was known to the Greeks from the carliest ages of their astronomical history.

Ancient Notions respecting the Movements of the Heavenly Bodies—
Copernican System of the Universe.

Although the nations of Western Asia observed the phenomena of the heavenly bodies from a very remote antiquity, they do not appear to have ascended to any general views respecting the system of the universe. It is to the astronomers of ancient Greece that we owe the earliest advances made in this respect. According to the system most generally prevalent among them, the earth was supposed to be placed immovable in the centre of the universe, while the sun, moon, and planets revolved around it in orbits of different magnitudes. The vicissitudes of day and night were explained by a revolution of the entire celestial sphere round the earth once in every twenty-four hours.

This system is generally denominated the Ptolemaic system of the universe, because it was adopted and expounded by Ptolemy, one of the most eminent astronomers of antiquity; but it is in reality of much earlier origin than the time of Ptolemy. It continued to form the basis of all astronomical researches down to the sixteenth century, when the true system of the universe was finally propounded in all its completeness by the immortal Copernicus.

It is a remarkable fact that several of the philosophers of ancient Greece were led to adopt views respecting the system of the universe which have subsequently been found to accord with the true state of nature. Their ideas, however, did not extend beyond the region of mere conjectural hypotheses, and they consequently failed to exercise any influence on the progress of astronomical inquiry.

It is said that Copernicus was originally led to entertain doubts respecting the Ptolemaic system of the universe, by his observations of the appearance presented by the planet Mars in different parts of its orbit. At one time the planet appeared almost as bright as Jupiter; at other times its light was so faint that it scarcely surpassed a star of the fourth magnitude. From this fact Copernicus concluded that it was impossible the earth could be the centre round which the planet revolved. Pursuing the train of his ideas, he was led to ponder on a statement contained in the works of some ancient writers, to the effect that the Egyptians supposed the planets Mercury and Venus to revolve round the sun, while they at the same time accompanied it in its annual motion round the earth. Again, some of the philosophers of ancient Greece supposed the sun to be in the centre of the planetary system, while the earth revolved in an annual orbit around it. Others of them, again, maintained that the diurnal revolution of the starry sphere was a mere illusory phenomenon occasioned by the revolution of the earth upon an axis in the opposite direction. Meditating upon these ideas and others of a similar kind, rejecting what was improbable, and adopting what appeared to him to be consonant to the simplicity of nature, he finally was led to propound the system which bears his name, and which has been universally adopted by the astronomers of modern times.

According to Copernicus, then, the sun is placed in the centre of the universe, while the

planets, including the earth, revolve around it in orbits of different magnitudes. The order. of succession of the planets, proceeding outwards from the sun, is this,-Mercury, Venus, the Earth, Mars, Jupiter, and Saturn. These were the only planets known in the time of Copernicus. Placed at an inconceivable distance from the solar system was the sphere of the fixed stars. The moon was supposed, as in the ancient system, to revolve in a monthly orbit around the earth. The diurnal motion of the stars from east to west was accounted for by attributing to the earth a rotatory motion on a fixed axis in the opposite direction, or from west to east, the axis being inclined to the plane of the earth's orbit at a certain definite angle.

CHAPTER III.

Explanation of the principal Circles of the Celestial Sphere - Determination of the Position of an Object by its Right Ascension and Declination; also by its Longitude and Latitude — Determination of the Position of a Place on the Earth's Surface.

This chapter will be devoted to an explanation of certain terms used in astronomy, and a description of the methods commonly employed by astronomers for fixing the position of an object in the celestial sphere.

The results of direct observation, as already remarked, indicate that the stars apparently revolve with a common angular motion round a fixed axis of the celestial sphere. The great circle of the sphere, which is perpendicular to this axis, is termed the equator. The extremities of the axis are termed the poles. Of these the pole which is elevated above the horizon in the northern hemisphere is termed the north pole; the other is termed the south pole, and is elevated above the horizon of any place in the southern hemisphere. It is obvious that when the north pole is elevated above the horizon, the south pole is depressed beneath it, and vice versa. The stars, in virtue of their apparent diurnal motion, generally revolve in imaginary small circles of the sphere, parallel to the equator. The apparent path which the sun annually describes in the heavens is termed the ecliptic. Like the equator, the ecliptic is a great circle of the celestial sphere. A diameter of the sphere, drawn perpendicular to the plane of the ecliptic, is termed the axis of that circle, and the extremities of this axis are termed the poles of the ecliptic. The equator and the ecliptic are inclined to each other at a certain definite angle. This angle is denominated the obliquity of the ecliptic. Its magnitude amounts in the present day to 23° 27' 5."5, but it is diminishing from age to age, although with excessive slowness. In the beginning of this century, which is an epoch frequently employed in astronomical computations, it amounted to 23° 27′ 55′′. The small circles drawn parallel to the equator, at the points where the ecliptic recedes most from the plane of that circle, are termed the tropics. The tropic of the northern hemisphere is termed the Tropic of Cancer. The tropic of the southern hemisphere is termed the Tropic of Capricorn. It will be seen that the equator and the ecliptic intersect each other in two opposite points of the sphere. One of these points, the point in which the sun is situate when it is passing from the south to the north of the equator, is termed the first point of Aries. The origin of this designation will be explained hereafter.

The earth may be considered as a sphere concentric with the celestial sphere, and having

analogous circles described upon its surface. The circles of the celestial sphere refer merely to apparent movements; the analogous circles of the earth have reference to the real movements of that body. The same remark applies to analogous diameters of the two spheres. Thus the diameter of the terrestrial sphere passing through the north and south poles indicates the axis around which the earth really revolves; the same axis, when prolonged to the heavens, becomes the axis of the celestial sphere, or the axis round which the stars apparently revolve. Similarly, the plane of the terrestrial equator, when extended to the heavens, traces out the celestial equator.

The various explanations which we have given here will be better understood by referring to fig. 1, Plate 1, but the student will find it to his advantage to consult carefully the circles described upon a celestial globe, and also those on a terrestrial globe.

An important part of astronomy consists in determining the positions of objects in the celestial sphere. Generally the position of a point on a spherical surface is ascertained when we know its angular distance from two great circles of the sphere whose planes are perpendicular to each other. Let P p represent the axis of the celestial sphere, P the north, p the south pole, E Q the equator, P E p Q a great circle passing through the poles, and meeting the equator in the points E, Q, where the ecliptic and the equator intersect each other. Let S represent the place of a star in the celestial sphere, and let P S p denote a great circle passing through the poles and the star. Finally, let us suppose E to represent the first point of Aries, as already defined. The circle PE p Q is termed the equinoctial colure. Now, if we

E

Q

assume as our circles of reference, the equator and the equinoctial colure, the position of the star S in the celestial sphere will be definitely fixed by means of its measured angular distance from those circles; in other words, by means of the arc E o and the arc S o. The arc E o is termed the right ascension of the star; it obviously measures the angle contained between the equinoctial colure and the great circle passing through the star. The arc S o is termed the declination of the star. Thus the position of an object in the celestial sphere is ascertained when we know its right ascension and declination.

If we had used for the circles of reference the ecliptic and a great circle passing through its poles and the first point of Aries, the position of the star would be determined by its distance from the first point of Aries, measured on the ecliptic, and its distance from the ecliptic,

measured upon a great circle passing through the poles of the ecliptic and the star. The former of these elements is termed the longitude of the star, the latter is termed the latitude. It was in this form that the ancient astronomers represented the position of an object in the celestial sphere.

Similarly the position of any place on the earth's surface is determined by means of its distance measured with respect to two great circles of the sphere perpendicular to each other. In this case the two reference circles are the equator, and a great circle passing through the poles, or a meridian, as such a circle is usually called. The distance from the equator is termed the latitude of the place; the distance from the meridian is termed the longitude. The equator has a determinate position on the earth's surface. It is otherwise with the meridian, of which any number may be drawn on the surface. Generally each nation uses for this purpose the meridian which passes through its capital city. Thus the longitudes of places in the British Isles are measured from the meridian of Greenwich; in France, the meridian of Paris is used for a similar purpose,-and so with other countries.

Measurement of Time-Apparent Motion of the Sun used for this purpose-Apparent Solar Time-Mean Solar Time-Sidereal Time-Equation of Time.

One of the most important practical advantages connected with the study of astronomy consists in its supplying us with an invariable standard for the measurement of time. In all civilised countries the subdivision of time is regulated mainly by the sun, the apparent motion of which exercises so important an influence on the daily concerns of life. And yet at first sight the sun would seem to be most unsuitable for this purpose. If we were to measure the length of the day by the time during which the sun is above the horizon, no standard could be more fallacious. In winter the days are short, in summer they are very long; in fact, throughout the whole year they are perpetually varying from day to day. In this respect the sun presents a striking contrast to the stars, the duration of whose respective courses above the horizon is invariable.

But let us take a more general view of the subject. Let us define the solar day to be the interval which elapses between two consecutive returns of the sun to the meridian. In this case again we encounter perpetual variations, although not so extensive as in the former instance. The length of the day thus defined does not deviate throughout the year to the extent of more than half a minute from the mean or average length of the days in the year. The mean solar day is on this ground used as the fundamental unit for the measurement of time. Each day is subdivided into twenty-four hours, each hour into sixty minutes, and each minute into sixty seconds. In this way we obtain days, hours, minutes, and seconds of mean solar time.

The day, as defined by the interval of time which elapses between two successive returns of the real sun to the meridian, is denominated the apparent solar day, in contradistinction to the mean solar day, which is the average of all the apparent solar days in the year. Similarly the time which elapses between two successive returns of a star to the meridian is termed a sidereal day. This interval of time, like the mean solar day, is invariable, and is in like manner subdivided into hours, minutes, and seconds.