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Sights are reduced (with a calculator, at least) by solving a spherical triangle with the vertices being the observer's DR position, the body's Geographic Position, and the "elevated pole," the pole, North or South, closest to the observers position.   Z is the internal angle of the vertex defined by the observer's position (ie, the angle from the pole towards the body at the observer's position).  

Zn is the angle, with respect to true north, to the body measured as one would measure a bearing.  There are then four differenct cases for calculating Zn depending on whether the body is east or west of the observer and depending on whether the observer is north or south of the equator.   For example, if the body is east of the observer (in the northern hemisphere) Zn = Z.   But if the body is west of an observer in the northern hemisphere, Z is the angle to the body measured counterclockwise from the pole and to get the usual "bearing" measured clockwise from the pole, Zn = 360 - Z.

In southern hemisphere, Zn = 180 - Z if body is east, 180 + Z if body is west.

Hope this helps.