17. Reference lines and circles.—As the stars move across the sky in their diurnal motion, they carry the framework of hour circles and equator with them, so that the right ascension and declination of each star remain unchanged by this motion, just as longitudes and latitudes remain unchanged by the earth's rotation. They are the same when a star is rising and when it is setting; when it is above the pole and when it is below it. During each day the hour circle of every star in the heavens passes overhead, and at the moment when any particular hour circle is exactly overhead all the stars which lie upon it are said to be "on the meridian"—i. e., at that particular moment they stand directly over the observer's geographical meridian and upon the corresponding celestial meridian.
An eye placed at the center of the earth and capable of looking through its solid substance would see your geographical meridian against the background of the sky exactly covering your celestial meridian and passing from one pole through your zenith to the other pole. In [Fig. 11] the inner circle represents the terrestrial meridian of a certain place, O, as seen from the center of the earth, C, and the outer circle represents the celestial meridian of O as seen from C, only we must imagine, what can not be shown on the figure, that the outer circle is so large that the inner one shrinks to a mere point in comparison with it. If C P represents the direction in which the earth's axis passes through the center, then C E at right angles to it must be the direction of the equator which we suppose to be turned edgewise toward us; and if C O is the direction of some particular point on the earth's surface, then Z directly overhead is called the zenith of that point, upon the celestial sphere. The line C H represents a direction parallel to the horizon plane at O, and H C P is the angle which the axis of the earth makes with this horizon plane. The arc O E measures the latitude of O, and the arc Z E measures the declination of Z, and since by elementary geometry each of these arcs contains the same number of degrees as the angle E C Z, we have the
Fig. 11.—Reference lines and circles.
Theorem.—The latitude of any place is equal to the declination of its zenith.
Corollary.—Any star whose declination is equal to your latitude will once in each day pass through your zenith.
18. Latitude.—From the construction of the figure
| ∠ E C Z + ∠ Z C P | = | 90° |
| ∠ H C P + ∠ Z C P | = | 90° |
from which we find by subtraction and transposition