AFAIK, the Nautical Almanac provides
celestial positions for the sun, moon, planet, and navigational stars. It does not include sight reduction tables. For these, you need a set of tables such as HO 214, 229, 249, etc. These are available for free download, as is the 2010 Nautical Almanac.
For the Noon Sight (latitude by meridian transit) you only need the Almanac. Here are the three cases:
Sight reduction tables are not required for these computations.
Case #1: When latitude and declination are of the same name, but latitude is greater than declination, use the formula:
Lat = (90̊ - Ho) + dec
Example: The DR latitude of a yacht at time of LAN is 40̊ N. The declination of the sun for that date and time is 20̊ 15.0' N. Since latitude and declination are both North (same name), but latitude is greater than declination, the above formula is used. Assuming the corrected sextant altitude (Ho) to be 69̊ 45', the solution is as follows:
Lat = (90̊ - 69̊ 45.0') + 20̊ 15.0'
and thus, Lat = (20̊ 15.0') + 20̊ 15.0' = 40̊ 30.0 North
Case #2: When latitude and declination are of the same name, but latitude is less than declination, use the formula:
Lat = dec - (90̊ - Ho)
Example: Assume the observer is in latitude 10̊ South and declination is 18̊ South. Since latitude and declination are of same name, but latitude is less than declination, formula #2 applies.
Case #3: When latitude and declination are of opposite names, use the formula:
Lat = (90̊ - Ho) - dec
Example: Assume the observer is in latitude 13̊ South and declination is 4̊ North. Since latitude and declination are of opposite names, formula #3 should be used to obtain observer's latitude.
Bill