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    Re: Makelyne et al
    From: Ken Muldrew
    Date: 2003 Jun 14, 12:02 -0600

    On 13 Jun 2003, at 21:06, Steven Wepster wrote:
    
    >  The main reason for Mayer's
    > success is that he managed to fit over 20 parameters in his theory to
    > over 200 observations of eclipses and occultations made after the
    > invention of the telescope. In my dissertation I want to answer (a.o.)
    > the question how he did the fitting, before the invention of the least
    > squares method.
    
    According to an article by P.J.G. Teunissen published in De Hollandse
    Cirkel, 2 nr. 1/2, April 2000 (but reproduced at
    http://www.ncg.knaw.nl/uk-site/Teunissen.htm)
    Mayer invented the method of averages for fitting arbitrary parameters.
    Briefly, if you have more equations than unknowns, you divide up the
    equations into as many groups as there are unknowns (a subjective
    procedure that makes the technique a bit dodgy), sum (or average) the
    equations in each group to produce n equations in n unknowns, and then
    solve for the unknowns. This was the first technique to incorporate all
    observations but it replaced the subjective act of throwing out some
    observations with the subjective act of grouping the equations (and so left
    room for improvement).
    Ken Muldrew.
    
    
    

       
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