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    Re: Bowditch Table 15
    From: George Huxtable
    Date: 2005 Jan 25, 14:00 +0000

    It seems that we're not yet finished with the Bowditch Table 15 (Table 9 in
    my earlier edition)
    
    I transcribed into emailese, writing A instead of Alpha, the expression in
    my edition (1981 vol 2) of Bowditch as-
    
    d = sqr { (tan A / .0002419 )^2 + ((H-h) / .7349) - (tan A / .002419) }
    
    in which d is the distance in nautical miles, A is the corrected vertical
    angle, H is the height of the top of the object above sea level in feet,
    and h is the height of the observer above sea level in feet. The constants
    .0002419 and 0.7349 are parameters which characterise the effect of
    terrestrial refraction.
    
    Is the expression and the text the same in later editions? Somebody please
    state, for my benefit, the expression for d as given in a more recent
    edition.
    
    I wrote- To me, it seems a bit suspicious that that text refers to "The
    constants .0002419 and 0.7349", although a third, and different, constant
    of .002419 also appears to be used in the expression. Is that a misprint, I
    wonder?
    
    But it seems me there's more wrong with the expression I quoted above than
    a simple matter of the number of decimal places in a constant term. When
    the angle =0, then the expression gives the same results as does the table,
    but the two seem quite inconsistent in the way they vary with the angle.
    
    I've no reason to believe that the numbers in the table are wrong (on the
    other hand, no reason to be certain that they are correct). But the numbers
    in Table 9 and the expression in the text for Table 9 are quite
    inconsistent.
    
    Just to check that my Table 9 and the later Table 15 are the same, here are
    two spot values to compare-
    angle = 0',  H-h = 100 ft., distance 11.7 miles
    angle = 1 deg 50', H-h = 450 ft., distance = 2.3 miles
    
    Does Table 15 give those same values?
    
    It strikes me that this must be a common problem in surveying, the angular
    elevation, above the true horizontal, of some object at a certain distance
    that's at a certain height above the observer, and the solution must be
    well-known. Otherwise, someone will just have to deduce it from first
    principles.
    
    George.
    
    ================================================================
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ================================================================
    
    
    

       
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