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).

Recovering Time From Known Position

An accurate correction to the chronometer time piece can be made using the time sight formula from a known position or confident DR position. A Casio pocket trig calculator will do a great job of time sight calculating. The Martelli Tables can be used to recover time also for navigators preferring to go old school.

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