Longhand Ex-Meridian

An ex-meridian is a sight reduction method for determining latitude when the bodies local hour angle (t) is near the meridian. A tabular correction can be added to the observed Ho so as to enable a reduction as if observed exactly on the meridian (LHA zero). There are quite a few tables out there that perform this task but most are multiple pages with multiple look-ups. To expedite the ex-meridian reduction process it is possible to use a one page custom table for a longhand solution by formula:

 +XM' = .5235 (t)(t)cos Lat cos Dec / cos Ho.

t = meridian angle degrees and tenths
Lat = assumed latitude
Dec = declination
Ho = observed altitude

Only two place precision is needed so a one page 10' natural cos sin trig table will work when combined with a custom factor (a) table.

Reworking the ex-meridian formula:

a = .5235 (t)(t)

+XM' corr. =  a(cos Lat)(cos Dec) / cos Ho

The (a) value is extracted from a very compact custom table (see attached). Cosine values are extracted from a one page 10' trig table (see attached). Round to two places for quick longhand reduction (see attached example).