The plane of the horizon, with the north, south, east, and west points, and the zenith, are represented as in Fig. 2. P and P′ are the poles of the celestial sphere, the dotted line connecting them representing the direction of the axis, both of celestial sphere and the earth. The circle Eq Eq′ is the equator. V is the vernal equinox, or the point on the equator whence right ascension is reckoned round toward the east. The circle passing through s, parallel to the equator, is a declination circle. The circle P s P′ is the hour circle of the star s. The arc of this hour circle contained between s and the point where it meets the equator is the star's declination. Its right ascension is measured by the arc of the equator contained between V and the point where its hour circle meets the equator, or by the angle V P s. The hour circle P V P′, passing through the vernal equinox, is the equinoctial colure. When this has moved up to coincidence with the meridian, N Z S, it will be astronomical noon. ] =7. Effects Produced by Changing the Observer's Place on the Earth.= The reader will recall that in Sect. 4 we described another system of circles for determining the places of stars, a system based on the horizon and the zenith. This horizon-zenith system takes no account of the changes produced by the apparent motion of the heavens, and consequently it is not applicable to determining the absolute positions of the stars on the celestial sphere. It simply shows their positions in the visible half of the sky, as seen at some particular time from some definite point on the earth. In order to show the changing relations of this system to that which we have just been describing, let us consider the effects produced by shifting our place of observation on the earth. Since the zenith is the point overhead and the nadir the point underfoot, and the horizon is a great circle drawn exactly half-way between the zenith and the nadir, it is evident, upon a moment's consideration, that every place on the earth has its own zenith and its own horizon. It is also clear that every place must have its own meridian, because the meridian is a north-and-south line running directly over the observer's head. You can see how this is, if you reflect that for an observer situated on the other side of the earth what is overhead for you will be underfoot for him, and _vice versa_. Thus the direction of our zenith is the direction of the nadir for our antipodes, and the direction of their zenith is the direction of our nadir. They see the half of the sky which is invisible to us, and we the half which is invisible to them.