Chris Lusby Taylor <[EMAIL PROTECTED]> writes:

> "Frans W. MAES" wrote:
> 
> > I know one more case of
> > an interesting bifilar dial. Using a pole style and a specially shaped
> > curve in the equatorial plane, one may obtain a polar dial with
> > straight, parallel E-W date lines, perpendicular to the hour lines.
> > This principle was described in the Bulletin of the Dutch Sundial
> > Society in 1979 by Th.J. de Vries.
> > [...]
> > http://www.biol.rug.nl/maes/zonwyzer/en/zwappi-e.htm
> >
> 
> This is an exciting sundial. Who would have guessed that you could achieve
> straight, parallel, date lines? Brilliant. Is the formula for the curve
> available, please? (Don't tell me - it's a catenary, right?)

The principle is relatively straightforward.  As the description says,
the pole style and base plate together constitute a polar dial.
(Since the second shadow is not needed to tell the time, I would
hesitate to classify this as a bifilar dial at all.)  At any given
time of day, the shadow plane will always cut the edge of the yellow
glass at the same point.  For different dates/declinations, the shadow
of this point will move up and down by the distance L*tan(D), where D
is the declination and L is the distance from the edge of the gnomon
to the edge of the shadow.  At noon, L must equal the height of the
style, H.  The trick is to make L = H for every time of day.  If x is
the distance from the base of the style, measured in units of H, and y
is the distance above the base plate in the same units, then the
equation for the necessary curve is this:  x = (1-y)*sqrt(1-y^2)/y

Have fun proving this!

--Art Carlson

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