This modified ex-meridian formula saves a few moves on the K&E slide rule (solution time 50 seconds).
Slide Rule:
a = (Cos Lat. Cos Dec.) / Sin (Lat. +/- Dec.)***
(+) contrary name (-) same name *
(+) contrary name (-) same name *
+XM' = .524 (a)(t)(t)
t = meridian angle in degrees and tenths **
t = meridian angle in degrees and tenths **
Calculator:
+XM' = (a)(t)(t) / 1.91
notes:
* The (a) value can be worked up prior to observation.
** Slide rule tip - pencil mark the slide C scale at .524 for quick cursor set.
*** Cos (Ho) can be substituted for Sin (Lat. +/- Dec.) Ho = corr. sextant altitude
*** Cos (Ho) can be substituted for Sin (Lat. +/- Dec.) Ho = corr. sextant altitude
+XM' = ex-meridian minutes of arc to be added to Ho then solve as a LAN observation.