Ever since being informed of the Time Sight - using the sextant as a sundial, I became curious of the accuracy to be expected from this type of observation.
In order to determine the variance between the exact longitude of the
observer and the longitude calculated by the Time Sight, I modified my program (written for practicing sun sights and containing high accuracy solar almanac) by adding a subroutine which used the calculated altitude of the sun (Hc) to calculate LHA and obtain LMT. Since the same equation is used to calculate both values, the theoretical variance should be zero. My interest was to see if other factors (besides Eqn-of-Time) affected the "zero value" and by how much. Enclosed graph shows the results of this calculation. I chose 21 June 2012 as the date in order to obtain the maximum range for the azimuth of the sun.
The results surprised me. I think that the recommendation in Bowditch(1906) of taking Time Sight near the Prime Vertical has more to do with the rate of change in sun's altitude than with the accuracy of the LHA.
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