Southern hemisphere celestial spheres
 

To clarify the ideas introduced in the previous sections, we consider the celestial sphere for an observer in the southern hemisphere. Let the latitude be ∅S. Then the celestial pole above the horizon is the south celestial pole Q. We proceed as follows:
1. Draw a sphere.
2. Insert the zenith, Z, and the horizon, NWSE, a great circle with Z as one of its poles.

Figure 1. A southern hemisphere celestial sphere

3. In figure 1 we have placed W on the front of the diagram. The convention that when facing north, west is on your left hand dictates the placing of N, S and E.
4. Insert Q, the south celestial pole, between the south point S and the zenith Z and such that the
altitude SQ of the pole is the latitude φ of the observer. We can then insert the north celestial pole P directly opposite.
5. Put the celestial equator in the diagram, remembering that P and Q are its poles.
6. Insert the observer’s meridian QZNP, according to the rule that it runs from the pole in the sky through the zenith and horizon to the pole below the Earth.
7. Put an arrowhead on the equator with HA beside it to show that the hour angle is measured westwards from the observer’s meridian.
Let us suppose we are interested in the position of a star X.
8. Draw the vertical ZXA and the meridian QXBP through its position. Then,
 

the azimuth of X = arc SE A = A^◦ E of S
the altitude of X = arc AX = a^◦
the zenith distance of X = arc ZX = 90 − a
the declination of X = arc BX = δ^◦ S
the hour angle of X = arc LB = Hh
the south polar distance of X = arc QX = 90 − δ.
 

Note: (a) that the azimuth is specified E of S to avoid ambiguity; (b) that the declination is labelled S again to avoid ambiguity.