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    Re: Interpolation of Meridional Part Table
    From: Ark Shvetsky
    Date: 2009 Mar 26, 16:23 -0700

    
    e is different.� 0.08181919 and 0.082271854 (this one is from� 
    Bowditch-1968).� Mr. Earle formula requires to use WGS84 value of e, whatever 
    it is.
    
    
    
    ----- Original Message ----
    From: "Christian "Eddie" Dost" 
    To: NavList@fer3.com
    Sent: Thursday, March 26, 2009 8:08:45 AM
    Subject: [NavList 7789] Re: Interpolation of Meridional Part Table
    
    
    The difference is in the factor A used in both examples.
    
    For WGS84 this is A = 6378137 / 1852 = 3443.9185
    in the second example this is A = 3437.7468
    
    The term inside the logarithm is the same for both examples.
    
    /Eddie
    
    George Huxtable wrote:
    > 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{at}hux.me.uk
    > or at +44 1865 820222 (from UK, 01865 820222)
    > or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    > 
    > 
    > 
    > > 
    
    -- 
    ___________________________________________________brainaid_____________
    Eddie C. Dost� � � � � Rue de la Chapelle 51� � � phone +32 87 788817
    � � � � � � � � � � � � B-4850 Moresnet� � � � � � fax� +32 87 788818
    ecd{at}brainaid.de� � � � Belgium� � � � � � � � � � cell� +49 172 9312808
    
    
    
    
          
    
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