In the first Section of Chapter II. we have already had occasion to consider the apparent daily motion of the sun in 24 hours, as arising from the rotation of the earth about his axis once in et. From the same cause, the whole heavens, comprehending the planets, comets and fixed stars, will appear to turn round in 23h 56' 4". As the stars are absolutely fixed, and have no motion of their own, they will always rise in the same point of the horizon, have the same meridian altitude, and set in the same place ; but they will appear to rise 3' 56" sooner every day, owing to their apparent diurnal revolution being performed 3' 56" sooner than that of the sun.
Since the planets, however, have a slow motion from west to east, their apparent diurnal rotation will not be performed exactly in 23h 56' 4"; and as they move in or bits considerably inclined to the earth's equator, they will rise in different parts of the horizon, have different meridian altitudes, set at different places, and continue for a longer and shorter time above the horizon. As these phenomena may be explained in nearly the same manner as the variations in the length of the day, and in the meridian altitude of the sun arising from the oblique position of the ecliptic to the equator, it would be unne cessary to dwell upon this subject. The orbit of every planet being inclined to the earth's equator, the distance of the planet from the equator or its declination must be perpetually varying, and occasioning varieties in its me ridian altitude, and in its continuance above the horizon.
While the earth turns round its axis, the two points in the heavens to which its poles are directed will ap pear at rest, Thus, if E Plate XXXIX Fig. 1. be the earth, HH the visible horizon of the place A, N the north pole of the earth directed to the point P in the heavens, and S the south pole directed to Ii, the points P, p will appear to be at rest ; and all the stars between P and H, called circumpolar stars, will move as it were round P, and will never descend below the horizon H. In like manner, the stars round the south pole fi, be tween H and fi, will never rise above the horizon H, while ad the intermediate stars will rise and set, and continue for different lengths of time above the horizon, in proportion to their distance from the equator EA. The circle comprehending the stars round the north pole P, which never set, is called the circle of perpetual ap parition; and the circle round the south pole ft, which contains the stars which never rise to any place, is call ed the circle of perpetual occultation. The time which
elapses between the rising of a star or planet, and its arrival at the meridian, is called its semidiurnal arch; the distance of the point of the horizon where a planet or star rises or sets from the east or west points of the horizon, is called its eastern or western amplitude; and the arch of the horizon intercepted between a ver tical circle passing through any star and the meridian, is called its azimuth,—the azimuth of a star when in the horizon being the same with the complement of its amplitude. Hence vertical circles passing through the zenith of any place, are called azimuth circles.
In consequence of the apparent motion of the sun among the fixed stars, all these bodies are related in their rising and setting to the tising and setting of the sun. A star is said to rise cosmically when it rises along with the sun, and to set cosmically when it sets as the sun rises ; a star is said to rise achronically when it ri ses as the sun sets, or when it sets along with the sun; and a star is said to rise heliacally, when it rises in the morning so long before the sun as not to be rendered invisible by the brilliancy of his light, and to set helia cally when it sets so long behind the sun as not to be ob scured by his beams.
We have already seen, that the apparent motion of the sun through the heavens arises from the annual motion of the earth round the sun. It was long suspected by astronomers, that when the earth was at one extremity of its orbit, the stars should appear in a part of the hea vens different from that in which they appeared when it was in the opposite point of its orbit. This change of place would evidently be equal to the angle subtended by the diameter of the earth's orbit at the nearest fixed star, which was called the parallax of the earth's annual orbit. Numerous observations were made to ascertain this an gle, but the result of all of them seemed to prove, that the stars are at such an immense distance, that the earth's orbit does not subtend at them a sensible angle. While Dr Bradley was engaged in observations of this nature, he discovered a vat iation in the position of the stars, called their aberration, which arises from the motion of light combined with the motion of the earth in its orbit. The history of this discovery has been given at length under the article ABERRATION, and therefore we shall confine ourselves at present to a mere explanation of the phenomenon.