I'd just like to say a few more things about the portable folded-paper
flat-dials. What interests me about them is that I like the Regiomontanus,
as my favorite portable dial, and the most easily-built sundial of any
category. But it's of interest how easily-built can be a portable-dial that
doesn't lose accuracy near noon. ...because that could matter for modern
urban applications, where public-transportation departures, appointments
and events might be near noon.
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I spoke of a 1-fold dial with a Horizontal-Dial on one surface and a
vertical Polar-Dial on the other surface. I said that it wouldn't work in
the manner that I'd described. I'd expected it to work with the top-edge of
the vertical section as the gnomon, when use tipped-up as a Polar-Dial with
both surfaces as polar-dial surfaces.
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But it would work fine using a nodus at the middle of the connecting-thread
(the thread that secures the right-angle fold). In that manner, it could
work as a Horizontal-Dial and a vertical Polar-Dial, or, tipped-up, it
could work as half of a Box Polar Dial.
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A 2:1 paper rectangle is folded at the middle of its long-dimension, to
make two mutually-perpendicular square surfaces. A thread connects the
middle of their outer edges, and that thread has a nodus at its middle.
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I call it the "corner-configuration" or "half-box configuration"
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With one square horizontal, that square would have a Horizontal-Dial, and
the other would have a vertical Polar-Dial.
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Or the dial could be tipped up to make both surfaces polar-dials.
.
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To summarize the 3 folded-paper dial-configurations that I've described:
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These 3 configurations each forms half of a right-square-prism, cut in half
by a plane through its axis (analogous to the half of a
right-circular-cylinder comprising a Cylindrical-Eauatorial Dial.
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With the 1-fold configurations, the user's thumb, resisted by the
connecting-thread, can hold the 2 surfaces apart at a right-angle.
...which worked fine for all of my corrugated-cardboard Tablet-Dials.
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Orientation about the vertical axis is by means of the declination-lines,
labeled by declination or (preferably) by the approximate date for each
1/12 of the year's ecliptic-longitude variation.
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1. Corner-Configuration or Half-Box configuration:
.
As described immediately above.
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With one plane horizontal, it mignt not be necessary to have a plumb-line
for leveling. With both planes polar, a plumb-line could orient the dial
about the NS & EW axes.
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2. Box-Configuration:
.
A 2:1 rectangle is perpendicularly folded-up a quarter of its length from
each end.
.
A thread connects the middles of the top-edges of the up-folded ends. The
nodus is at the middle of that thread.
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Disadvantage:
.
The 3 folds complicate things for a folded-paper dial. ...in the matter of
holding the up-folded ends perpendicular to the base. That adds a whole
qualitatively different design problem to a folded-paper dial.
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Advangage:
.
Potentially convenient use, by its resemblence to Cylindrical-Equatorial
and especially to a Box-Polar (...which is what it is when tipped up as a
Polar-Dial).
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Orientation with respect to EW & NS axes is as for the corner-configuration.
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3. V Configuration:
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A 2:1 or 1:1 paper square is folded at-middle into a right-angle V.
...hand-held, with the fold-crease in the plane of the meridian, with the
two dial-planes tipped equally from the plane of the meridian.
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As with the Corner-Configuration, the right-angle is held by a thread
connecting the middles of the outer-edges of the two sections. The user's
thumb holds the two planes apart, resisted by the connecting-thread.
.
-
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Each of these 3 configurations can be used in either of 2 orientations:
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Horizontal:
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One plane, or at least some of the edges, is/are horizontal.
.
Polar:
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All of the planes are polar, parallel to the Earth's axis.
.
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Those combinations of configuration and orientation make 6 possible
portable folded-paper flat-dials.
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I'm not claiming that others aren't possible.
.
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The 1-fold configurations would be much easier to build, given the problem
of keeping the box-configuration's two up-folded ends perpendicular to the
plane between them.
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In the horizontal-orientation, the corner-configuration looks easier to use
than the V-configuration, because the corner-configuration has a horizontal
surface, giving it easier leveling even without a plumb-line. (My
Tablet-Dials were all 5-minutes-accurate without a plumb-line or
spirit-level.)
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Especially for the polar-orientation, the V-configuration has appeal.
...though, even there, the corner-configuration might be easier to orient
about the polar-axis, due to the ramp-like orientation of one of its planes.
.
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Of course, for the dials in polar-orientation the line-construction is much
easier to explain. In fact, it practially doesn't need any explanation.
.
T
