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    Lunars and logarithmic differences
    From: Ottfried Thümmel
    Date: 2014 Dec 13, 12:31 -0800

    Logarithmic differences are used in nearly all strict methods for clearing the lunar distance. In my opinien Dunthorne himself was the first in publishing a table of the logarithmic differences in the 1766 issue of "Tables Requisite to be Used with The Nautical Ephemeris for Finding the Latitude and Longitude at Sea". Recently Bruce Stark gave tables containing the logarithmic differences in the "Stark Tables" (there the logarithmic differences are denoted by letter Q). What I am wondering are the table values in the Dunthorne tables and the Stark Tables as well. The logarithmic difference is defined as log (cos H / cos h) where H is the true altitude and h the apparent altitude. For example, assume the apparent altitude h of the moon to be 40° and the horicontal parallax 53', then by table 2 (Stark Tables) the difference between the apparent and the true altitude is 39.46'. Calculating log [cos (40° + 39.46')/cos(40°)] I get 423.2 versus the tabulated value 411.00 (interestingly, the difference between the so calculated value and the tabulated value is always approximately 12.2). Dunthorne gave 411.3 in his table. What is the reason for the difference between the calculated and the tabulated values?

     

     

       
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