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To answer the original question: while I have owned a copy of “Stark Tables for Clearing the Lunar Distance”, 3rd rev’d ed. (2010) for almost seven years, I confess that I’ve yet to put in the grind to learn how to use them. If the ongoing Covid-19 restrictions continue throughout the current year (perish the thought!), perhaps I will run out of excuses and finally get stuck in.
P.S. Might be of interest: a reasonably-detailed explanation of how to clear lunar distances is contained in John Letcher’s “Self-Contained Celestial Navigation with H.O. 208” (1977), pp. 87-95. Helpfully, several questions are posed to confirm the reader’s understanding (answers are supplied at the end of the book).
P.P.S. Letcher’s book contains a separate chapter entitled “Time by Lunar Lines of Position” (pp. 9-106). Below are introductory paragraphs explaining the concept:
“The basic idea is to check whether lines of position from moon sights agree in longitude with lines of position from sights of other bodies. As long as the chronometer is right, the moon will attest to the fact by being in the right place in the sky, so lunar lines of position are consistently in agreement with sun and star sights. If the chronometer is wrong, and you work the sights as if it were right, the moon lines of position will lie consistently to either the eastward or westward of the other lines, depending on whether the chronometer is fast or slow on GMT? Again, we are using the relatively rapid known motion of the moon as a time standard, but in this procedure, we measure its motion relative to the horizon by an ordinary altitude sight. In case the lunar line is found to disagree with the other lines, a time can be found that will bring them into agreement, and this procedure finds the true GMT and chronometer error just about as accurately as lunar distance sights would....
“[R]easonably accurate time can be found if good, accurate altitudes are taken of the moon and the other bodies. The moon and other sights are worked and plotted into lines of position by completely standard, habitual methods, but for this purpose it is essential to work to very high standards of accuracy attainable: care in taking the sights, and applying sight corrections, carrying the tenth of minutes throughout, and plotting with great precision.”
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