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    Re: Meridional Distances
    From: Sam Chan
    Date: 2002 Sep 17, 21:51 -0700

    The formula in Bowditch uses a series expansion. A closed form derived in
    Williams is
    
    M(psi) =  a * Ln (Tan(pi/4 +abs(psi)/2)) - (a
    e)/2*Ln{(1+e*sin(abs(psi)))/(1-e*sin(abs(psi)))}
    
    where
    
    psi is the Geodetic Latitude
    a is the length of the semi-major axis
    e is eccentricity.
    
    For those who really want to know, the equation for the Meridional Distance
    (Distance along the arc of a meridian on the surface of an ellipsoid) as
    given by Williams is:
    
    L(psi) = integral from 0 to psi of (a[1-e^2])/sqrt([1-e^2 sin^2(psi)]^3)
    d(psi)
    
    No closed form solution to this integral can be had so a numerical solution
    must be used.
    
    Sam Chan
    ----- Original Message -----
    From: "Chuck Taylor" 
    To: 
    Sent: Tuesday, September 17, 2002 9:20 AM
    Subject: Re: Meridional Distances
    
    
    > >
    > > Although I have tables accurate to 2 decimal places for the Meridional
    > > Parts, the Meridional Distances come only in whole degrees, so need to
    > > be interpelated for in-between values.
    >
    > Peter,
    >
    > Bowditch has tables of Meridional Parts to quite a number of decimal
    places.
    > The method for computing distances using Meridional Parts is called
    "Mercator
    > Sailing" and is also described in Bowditch.
    >
    > The introduction to the tables in Bowditch gives a formula for computing
    > Meridional Parts.  I have programmed this into a calculator.  One could
    also
    > program it into a spreadsheet.  If memory serves me correctly (I'm away
    from my
    > home library) there is a typo in the formula in Bowditch 95, but Bowditch
    80/84
    > Volume 2 has it right.
    >
    > Best regards,
    >
    > Chuck Taylor
    > Everett, WA, USA
    
    
    

       
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