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    Re: AP terminology
    From: Hewitt Schlereth
    Date: 2009 Nov 13, 20:12 -0400

    Hey, guys, didn't Capt. Sumner take one sight of the sun around 10
    a.m. and then ASSUME three different LATITUDES (not longitudes) to
    plug into a time-sight formula?  HS
    On 11/13/09, P H  wrote:
    > Since LOPs are one-dimensional objects, you need precisely one parameter to
    > characterize them.  It is this parametrization that amounts to "calculating
    > the LOP directly" (answer to Geoffrey Kolbe's question).  Sumner used
    > longitude as the parameter.  The parameter doesn't have to be longitude and
    > in the case of LOP=meridian, it is in fact unsuitable.
    > The LOP is what it is, based on the Ho and GP, independent of any AP.  As I
    > said in an earlier post, you need to have a coordinate system to do anything
    > practical.  The AP is the origin of such a convenient local coordinate
    > system.  We have some freedom in choosing where to place this AP=origin.
    > The computed intercept distance then tells us how far the chosen AP is from
    > the LOP, and the computed azimuth tells us the orientation/direction.  That
    > is what the solution of the celestial triangle AP-GP-Pole is about; it gives
    > the relative position of the (independently existing and fixed) LOP and our
    > arbitrarily chosen AP.  In practice St. Hilaire proceeds in reverse; we
    > choose the AP first, solve the triangle, and then we construct the LOP at
    > the appropriate distance from the AP and orientation with respect to true
    > North.
    > On a Mercator plotting chart LOPs look like straight lines (for not too high
    > Hs's).  A straight line lying in a plane can be defined by two points, or by
    > one point and one direction.  Sumner uses the former; St. Hilaire uses the
    > latter.  St. Hilaire is less work because one detail regarding the direction
    > part is automatic; it is the angle between the LOP and the azimuth line
    > toward the GP, which is always 90 degrees.  We can therefore plot the LOP at
    > the right angle to the azimuth line (at the intercept distance) because
    > Mercator mapping used in plotting charts is conformal, i.e. it preserves
    > angles.
    > Peter Hakel
    > ________________________________
    > From: John Karl 
    > To: NavList 
    > Sent: Fri, November 13, 2009 12:33:27 PM
    > Subject: [NavList 10635] Re: AP terminology, WAS: 2-Body Fix -- take three
    > No one has addressed my question of why the St Hilaire method
    > calculates an altitude at a location our ship is NOT at, when we've
    > just measured the altitude where our ship IS at.  (For politically
    > correct reasons, I'm not using the name of this location.)
    > Now lets go back to Sumner's 1837 calculation, where he picked three
    > different longitudes and calculated three points on the circular LOP.
    > This calculation is exact, and the equation for each point is the same
    > as the one of the two necessary in the St Hilaire method (thus each
    > Sumner point is half the work of a St Hilaire reduction).  And he
    > could calculate as many exact points as he wished.
    > So I'll put my question yet another way:  Why is the St Hilaire method
    > superior to Sumner's and consequently the only one used today??
    > I claim that the answer to this question has been made confusing
    > because of the conventional name (names?) used for the location of the
    > St Hilaire altitude calculation.  As evidence of this confusion I note
    > that some authors write that we need to assume some point because the
    > distance between the GP and the LOP is too great to plot, that there's
    > insufficient information to plot the LOP, or that iterations are
    > required to get exact points on the LOP.  The Sumner calculation
    > demonstrates that none of this is correct.
    > JK
    >  >
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