Aye that makes sense.
I hate to badger you with my busy work, but I'm unsure of Antares from my worksheet attached above.
Antares using a nautical almanac and Ho229 tables I work out:
Hc 7* 52.5'
Ho 7* 14.1'
---------------
+ 38.4 (measure 38.4nm AWAY from Antares)
But using
USNO numbers the Hc for Antares is
7* 32.1' Why does mine differ so greatly?