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    Re: Poor St. Hilaire
    From: John Karl
    Date: 2007 Oct 17, 12:23 -0700

    Ok, one last try on Poor St. Hilaire, using a different approach:
    We can say that the St. Hilaire intercept method is a process
    (containing both computational and graphic components), perhaps
    thinking of it as a machine.  It has inputs and outputs:  We feed in x
    and y, the latitude and longitude of a point, let's call it the RP
    (the reference point).  For every x and y that's input to the process,
    out comes another pair of coordinates, the lat and lon of a point on
    the celestial LOP.  Let's call this point SHP (St. Hilaire point) for
    convenience of discussion.  The SHP is the unique point closest to the
    RP that is exactly on the LOP.
    Some List members will recognize that the above descrinption is close
    to mathematical phraseology:  The St. Hilaire method is a function
    F(x,y) with inputs (independent variables) x and y.  You feed in these
    coordinates of the RP.  Out comes the coordinates of a point exactly
    on the LOP, which we're labeling the SHP.  You can find as many points
    on the LOP as you like, tracing out the LOP - exactly.
    Now for comparison, consider the hull speed of a displacement boat, Hs
    = 1.34 sqrt(Lw), where Lw is the waterline length (in feet) and Hs is
    the hull speed (in knots), and sqrt means take the square root.  This
    also represents a function, a process, or a machine, however you want
    to look at it.  You input Lw, out comes Hs.
    Now the major point:  If we wanted to plot the hull speed versa the
    waterline length, would we call the waterline length an estimate?
    Would we call it an assumed Lw??  NO.  It's called an independent
    variable,  meaning we can specify any Lw we like and we get the
    corresponding Hs.  There is no estimation, no uncertain reckoning, no
    assumptions in specifying Lw.  The same is true for the specifying St.
    Hilaire's RP.  We SPECIFY a point where we wish no know the nearest
    point on the LOP.  No estimation, no assumptions.
    Now if members think that this is unnecessary and unproductive nit-
    picking of terminology, consider that:
    1.  All CN books (well, all that I have seen) either don't attempt to
    explain the reason for the assumed position, or they explain it
    incorrectly.  For example, some say that an assumption is necessary
    because the distance between the sun's GP and the ship is too great to
    plot, some because there's insufficient information to plot the LOP,
    and others because we don't know how to plot the exact LOP.
    2.  A List member has stated that the accuracy of the St. Hilaire
    result depends on how good the initial estimated position is.
    3. And therefore the St. Hilaire method is really an iterative method.
    We've just seen that all of this is wrong.  This misunderstanding may
    not stem from the unfortunate terminology of "estimated" position and
    "assumed" position.  But if it doesn't, where does it come from??
    John Karl
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