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    Re: Possible limitaion for lunar distance measuremen
    From: George Huxtable
    Date: 2009 Mar 1, 20:56 -0000

    Thanks to Kent Nordstrom for supplying the Dunthorne formula that the old 
    German navigation manual considered so lacking.
    
    I can confirm that the formula provided appears to correspond with the 
    procedure described in words by Dunthorne in Maskelyne's first edition of 
    "Tables requisite ..." of 1766.
    
    Dunthorne provides a justification of his procedure which I admit to being 
    unable to follow. However, I've always thought that procedure to be 
    geometrically exact (assuming a spherical Earth, anyway) , without having 
    any good basis for that confidence. If the Lehrbuch provides any reasoning, 
    or examples, to justify their distrust, at lunar distances departing from 
    near-90�, it would be interesting to learn.
    
    Does that distrust stem from defects in the Dunthorne formula itself, or 
    perhaps in the tables and arithmetic procedures that are used to implement 
    it?
    
    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.
    ----- Original Message ----- 
    From: "KENT AE NORDSTR�M" 
    To: 
    Sent: Sunday, March 01, 2009 10:53 AM
    Subject: [NavList 7487] Re: Possible limitaion for lunar distance measuremen
    
    
    Referring to [7465] from Frank Reed, [7471] from Wolgang K�berer and [7477] 
    from George Huxtable. Thanks for providing your views on the possible 
    limitations in distance when using the Dunthorne formula. And thanks to 
    Wolgang, who translated the text from the German manual much better than I 
    did. I am not aware what Wolgang will do - ref to George's question - so I 
    provide the formulas without any intention to interfer in Wolgang's effort.
    
    
    
    The formula no.18 in the German manual, page 386:
    
    Quote
    
    
    
    cos D' = cos ?' +  cos m' * cos s'  * ( cos D - cos ? )
    
                                   cos m * cos s
    
    
    
    (Formel von Dunthorne)
    
    Un-quote
    
    
    
    In the above formula:
    
    D' = true distance
    
    ?' = H' - h', true values of altitudes
    
    m', s' = H', h'
    
    m, s = H, h, apparent values of altitudes
    
    D = apparent distance
    
    ? = H - h, apparent values
    
    
    
    These designations have been taken from another issue of the German manual, 
    I don't know which because I just have copies of some pages from these 
    manuals.
    
    
    
    The formula no.20
    
    Quote
    
    
    
    cos D' = cos ?' - 2 *  cos m' * cos s'  * sin � ( D + ? ) * sin � ( cos D - 
    ? )
    
                                        cos m * cos s
    
    
    
    Un-quote
    
    
    
    That is, the formula no.20 is the same as no.18 but put into another form.
    
    Kent N
    
    
    
    
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