Quicker Ex-Meridian Formula

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  *

+XM' = .524 (a)(t)(t)      
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

+XM' = ex-meridian minutes of arc to be added to Ho then solve as a LAN observation.