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Recently, I thought it would be interesting to turn back the calendar about half a century, and try to perform a sight reduction without an electronic calculator, using a pencil-and-paper-and-tables method instead.  It worked well, though it took me much longer than if I had used a calculator - I suppose the process becomes faster with practice.

The introduction pages of Pub. 229 include the formulas used to compute the values of altitude Hc and azimuth angle Z tabulated in the main pages (see page xxv, appended).  Ten months of coronavirus lockdown can have strange effects, such as inducing one to read the introduction to Pub. 229.  The formula for Hc can be easily derived from the cosine formula for spherical triangles.  In contrast, my very rusty memories of spherical trigonometry were inadequate to allow me to derive the formula for Z:

tan Z = (cos d sin LHA) / (cos L sin d - sin L cos d cos LHA).  

I would be very grateful if anyone would could point me to a reference that contains the derivation of this formula.  Many thanks in advance.

Rafael C.Caruso