The Mathematics of the Longitude - Department of Mathematics

Star's altitude
Lunar distance
Horizon
Figure 8.2 A Lunar distance observation.
(2) Calculate the mean of measured angles and LMT of the
observations made. That is to say, the sums of the lunar distances,
the moon's altitudes, the sun or the star's altitude, and the LMT
should be divided by the number of sets. By so doing, small errors
of observation are eliminated or reduced.
(3) Use LMT and EoT, obtained from the almanac, to find the Local
Apparent Time (LAT).
LAT = LMT + EoT
Moon's altitude
(4) Obtain the True Lunar Distance by clearing the mean of the
measured lunar distances in (1) of the effects of refraction and
parallax (Section 8.3). It is at this moment that we need the altitude
of the moon and the altitude of the stars or the sun in order to
ascertain the exact values of the refraction and parallax for the
moon and sun or refraction for the stars.
(5) Find Greenwich Apparent Time (GAT) from the True Lunar
Distance in (4) by interpolation in the lunar-distance tables in the
almanac.
(6) The LONGITUDE is the difference between Local Apparent Time
in (3) and Greenwich Apparent Time in (5).