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    Re: Coastal Plotting Sheets
    From: Bill Noyce
    Date: 2007 Mar 28, 10:16 -0400

    On 3/28/07, Bill  wrote:
    > > From: Michael Bradley 
    > > To do the geometry, you draw a 'base line' between the
    > > two known objects, take 90 deg minus the observed
    > > angle = x, draw a line from each object at angle x to
    > > the base line. Where these two lines meet is the
    > > centre of the circle, which you can then draw with
    > > your compasses. If your drawing is accurate, the
    > > circle passes through the fixed objects.
    > I'm lost here.  If I draw a line segment between the two points, as I
    > perceive it the rest is about impossible.
    Perhaps the confusion is the phrase "draw a line ... TO the base line."
    What Michael means is compute 'x'=90-(observed angle), then draw a
    line from object 1, extending out to sea, and forming angle 'x' with
    the baseline.  Draw a similar line from object 2.  You now have an
    isosceles triangle, with the two base angles = 'x', and the "point" is
    the center of your circle.  Use either of the two equal sides of that
    triangle as the radius when drawing the circle.
    If the original observations were made with a compass, of course this
    technique throws away useful information -- namely, the bearings to
    each object.  Perhaps it would be useful to draw all the reciprocal
    bearings on a transparent sheet, along with a North reference, and
    then slide the sheet around on the chart *keeping its orientation
    correct*.  In this case, you probably won't find a way to place the
    sheet so all the lines go through their landmarks and the North
    reference matches too.  Try to minimize the error (minimax, or
    least-squares, or something, by eye), and you'll have a fix and some
    idea of how trustworthy it is.
        -- Bill N.
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