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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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