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    Re: Interpolation of Meridional Part Table
    From: George Huxtable
    Date: 2009 Mar 26, 14:47 -0000

    The plot thickens-
    
    Andres calculates, from the expression he gives in [7784]
    
    WGS84
    
    a = 6378137 [m] = = 6378137/1852 [nm]
    
    f = 1.0/298.257223563
    
     The result is:
    
    MP( 45.000000 ) = 3019.058271357112100000
    
    The expression Andres quoted used eccentricity (epsilon) rather than the 
    flattening f that he tells us is f = 1.0/298.257223563 for WGS84. However, 
    we can deduce one from the other using the expression given in Meeus, in 
    which
    eccentricity = square root of ((2 * f)  - (f * f)) for which I have taken 
    the result to be 0.08181919, exactly in keeping with Earle's figure.
    
    ===========================
    
    On the other hand, I have tried to do exactly the same thing with my pocket 
    calculator and with the following values, taken from Earle-
    E= 0.08181919
    A = 3437.7468, the Earth's equatorial radius in geodetic miles.
    Latitude L= 45
    
    and here's a transcription of the equation I've used, now corrected, which 
    runs on a 20-year-old Casio programmable calculator-
    M=A*LN(TAN(45+.5*ABSL)*((1-E*SINABSL)/(1+E*SINABSL))^(E/2))
    
    and that gives me M(45�) = 3013.648, which conforms with Bowditch, and not 
    (quite) with Andres..
    
    Why do Andres and I differ (slightly), and why do I agree with Bowditch, 
    when Andres and I are trying to calculate the same thing with the same 
    quantities, using what appears to be the same expression?
    
    You can see that I've rejoined the nit-picking purists, as my natural home.
    
    George.
    
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
    
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