A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Greg Rudzinski
Date: 2014 Oct 5, 10:19 -0700
See attached excerpts of table 24 and 25 that covers the full range of Sun declination. For today at 34° north a=2.6 . Looking in table 25 under the (a) value of 2.6 the furthest out an ex-meridian can be observed will be 24 minutes 40 seconds from LAN. This means a 49 minute window is available to observe Sun ex-meridians using this table.
For example if observing the Sun 24 minutes before LAN today from 34° N there will be an ex-meridan value of 25' to add to Ho to then solve as a LAN. Interpolation is required to get this value. It may be easier to use a calculator using the (a) value and the formula (a)(time^2) / 60 = (2.6)(24)(24) / 60 = 24.96' correction to add to Ho. Or use (.267)(a)(LHA^2) = (.267)(2.6)(6)(6) = 24.99' correction to add to Ho
Notice that the ex-meridian correction is only 0.7' when 4 minutes from LAN. If precision is only needed to 1' then you will have an 8 minute window to observe LAN without worrying about adding a correction.
I will try for a real example later today. The down side is that the further you are in time from LAN then the less accurate will be the ex-meridian when compared to a standard LOP reduction for the same observation.