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    Re: Mendoza's method for clearing lunars.
    From: Frank Reed CT
    Date: 2004 Aug 2, 18:44 EDT
    As I noted on this list three months ago, the 1828 edition of Norie is available online at the Mystic Seaport Library. It is COMPLETE (including Table XXXV).

    Here is a link to the digital collection:
    http://www.mysticseaport.org/library/initiative/MsList.cfm

    Scroll down the list to "N". You will find "New and Complete Epitome of Navigation" by Norie, J.W. 1828. Follow the link. Then scroll down to "Tables". All of the tables are lumped together. Table XXXV starts on page 224.

    But you don't really need the original. As I noted on this list two months ago, Table XXXV is nothing more than a tabulation of the quantity (1/2)*cot(d)*x^2 where d is the lunar distance, and x is the other angle (either correction). That's all it is! Note that if you want the values in seconds of arc at the end and the angle x is in minutes of arc (as it is in the published table), then you need to divide by 57.3 (degrees in a radian). Clearly it is EASY to punch up any values from Table XXXV you may require on a handheld calculator or in a spreadsheet or other software.

    Most of the series methods, Witchell's, Mendoza Rios, Bowditch #1, etc. require the calculation of two linear terms and (usually) one quadratic term. As I described in my post on "Easy Lunars" (available online at www.historicalatlas.com/lunars ), the corrected distance  d' is found from the uncorrected distance d via
       d' = d + A*dh1 + B*dh2 + Q.
    That's two terms that depend linearly on the altitude corrections, dh1 and dh2, and one term that depends quadratically on dh1 (other quadratic terms are not necessary because they're very small). Details on tha A and B factors at the link above, but for now it's worth knowing that Q is given by
       Q = (1/2)*cot(d)*dh1^2*(1 - A^2).
    If you multiply this out, you find that you have two terms:
       Q = (1/2)*cot(d)*dh1^2  -  (1/2)*cot(d)*(dh1*A)^2.  
    So this means that we can get Q by entering a table of (1/2)*cot(d)*x^2 twice --once with the Moon's altitude correction and then again with the Moon's linear term which we have already calculated.

    See??

    Frank R
    [ ] Mystic, Connecticut
    [X] Chicago, Illinois
       
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