When you have a calculator or computer handy, sight reduction tables are obsolete. However, if you don't have electronics handy, or don't trust them, or just want to do it the traditional way, then you need the sight reduction tables.
Sight reduction tables are simply pre-computed solutions to various problems in spherical trigonometry.
Each entry in the sight reduction table uses an observer's latitude, a celestial declination, and a local hour angle as inputs, and produces computed altitude (Hc), computed azimuth (Z) and correction factor (d).
To produce tables for all reasonable values of these three inputs would require a library full of books full of tables. Therefore, the inputs have all been rounded to the nearest degree. In this way, the tables are reduced to six volumes. The standard sight reduction set is a publication known as HO 229.
(Other formats are available. The military sight reduction tables for air navigation are available for free download.)
One sample page from the sight reduction table is (approximately) reproduced here. To use these tables, you find the page corresponding to the latitude of your assumed position. Next, you use the declination of the celestial body to select a column. Finally, you find the local hour angle of the celestial body you're sighting on and use that to select a row from the table.
This return three values:
See introduction for sources of published sight reduction tables.
New: this is an editable table. Simply enter the latitude, first declination, and specify same or contrary declination name from latitude.