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    John Franklin lunar from 1818 and Mendoza y Rios method
    From: Modris Fersters
    Date: 2021 Jul 31, 09:04 -0700

    Hi, everyone who is interested in historical lunars!

    Here is link to J.Franklin lunar observations from 1818 (full calculations, original documents). Very interesting!     

    https://cudl.lib.cam.ac.uk/view/MS-FIS-00003/1

     Calculations are made on printed forms. These forms were printed in 1814. Here is link to e-book:  

    https://books.google.lv/books?id=ZWpbAAAAQAAJ....

    The method used by Franklin is that of Mendoza y Rios. I found two different methods from him: one published in 1801, other in 1809. The first method link to e-book is here:

    https://books.google.lv/books?id=FzIAAAAAQAAJ&redir_esc=y

     The second method link to e-book:

    https://archive.org/details/b22007659

     

    These methods are fundamentaly different. Tables are also absolutely different. Of course, the second method is most advanced: only addition operations are necessary, there are no half sums or differences which makes calculations liable to errors.

    Franklin used the second method (that from 1809). This method is very convenient. I tried to use these Mendosa y Rios tables and found that the process of clearing lunars takes about 7…10minutes. Only Thomson method published later (in 1825) allows me clear lunars a little bit faster (6…9 minutes). But there is one advantage in Rios method: it is possible to clear distances larger than 120 degrees.   

    I am not surprised that Mendoza y Rios method was widely used in Royal navy and East Indian service (at least this is claimed in one letter from the beginning of 19. century).

    I recalculated some Franklins lunar clearings by the same method he used and found some errors. For example May14,1818 (second set) Franklin makes mistake in corrected sum of altitudes. This yields to 1 minute error in cleared distance. Franklins cleared distance: 104 35 50; I cleared by Mendoza tables: 104 36 56; cleared by F.Reed lunar calculator: 104 36 54.

    Besides Franklin always uses altitudes to nearest seconds, but this method needs input altitudes only to nearest minutes. I found that Franklin sometimes even unnecessarily interpolates logarithmic values from tables to match the seconds in altitude values.

    Modris Fersters

       
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