In order to understand the problem we need to know something about the astronomical triangle. The astronomical triangle is formed by three points on the celestial sphere: the north celestial pole, the zenith and the star being observed. The angle that is of particular interest to us here is the angle subtended at the star between the pole and the zenith, i.e. the angle pole-star-zenith. This angle is known as the parallactic angle and is usually designated by the letter q. The parallactic angle increases as the hour angle increases. When a star is on the meridian q = 0 if it is on the equatorial side of the zenith, but q = 180° if it is on the polar side. The reverse is the case for an observer in the southern hemisphere.
The parallactic angle of a star changes in the course of the night, due to its diurnal motion. Its value at any time, i.e. for any hour angle of the star, is given above in the section on calculating the effects of atmospheric refraction.
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