I'd like to correct a few errors I've made, and make a few more comments. . --------------- . Just as the cross-section of a Cyindrical-Equatorial Dial is a half-circle, the ideal cross-section of a Box-Polar Dial or the Horizontal/Polar combination that I proposed, would be a half-square. . So the piece of paper starts as a 2:1 rectangle, with its end-quarters folded up at a right-angle (and secured there by a connecting-thread with a nodus at its middle). ...resulting in a half-of-a-square cross-section. . The dial that I called "V-Twin Reclining-Declining" (could also be called "V-Twin EW-Reclining")also has a cross-section that's half of a square. The difference is that, with the Horizontal/Polar, the half-square sits on one of its edges, and with the V-Twin, the half-square sits on one of its corners. . If their axes were tipped up, to be parallel to the Earth's axis, both of those would become square Polar analogs of the Cylindrical-Equatorial. . --------------------- . Any non-declining Flat-Dial (including the Horizontal-Dial) could have those two Vertical-Polar dials added to its sides. If those Polar-Dials' top-edges are horizontally-trimmed, on a plane passing through the nodus, then declination will be shown whenever the Sun is up. ...the advantage of Horizontal-Polar over ordinary Horizontal. . Of course the same all-day hours-range is acheived with a Cylindrical-Equatorial, if its top-edge is trimmed horizontal on a plane passing through the nodus. . Because it directly shows solar-time and solar-declination, and doesn't need any explanation, the horizontally-trimmed Cylindrical-Equatorial is my favorite stationary-dial. . Similarly-trimmed top-edges would allow a Box-Polar Dial, too, to likewise tell time and declination whenever the Sun is up. . --------------------- . Box-Polar Dials (Polar-Dials with added sides perpendicular to the usual polar surface)are sometimes made universal, by having pivot for tipping the bottom polar-surface to an angle equal to the latitude. Of course then it isn't possible to have the horizontally-trimmed top-edges, and so such dials can only tell time and declination from 6 a.m. to 6 p.m. . Of course the same would be true of a similarly universal Cylindrical-Equatorial. . In their defense, of course a lot of locations are shaded outside of that hours-range anyway. . --------------------- . Of course then a portable Box-Cylindrical-Dial, too, could be universal, with either a plumb-line attached to the connecting-thread, or to each of the vertical sides, or by aligning your latitude on a latitude-arc with the horizon or a distant point whose height is equal to that of the dial. . Similarly, just as Horizontal-Dials made for a particular latitude were sometimes made universal by tipping, the same could be done with a Horizontal-Polar dial. ...the tipping being achieved as described in the previous paragraph. . In both instances of course, with the top-edges no longer horizontal-trimmed, both of those dials would only read from 6 a.m. to 6 p.m. . -------------------- . In a recent post I mentioned a 1-fold version of Horizontal/Polar. It wouldn't work in the manner that I described, but it could work. But it would be troublesome. . My favorite of the non-universal folded-paper flat-dials is Horizontal-Polar: . A 2:1 paper rectangle is folded up perpendicularly at its outer quarters, to make a half-square cross-section. ...secured by a thread connected the the middles of the top-edges of the up-folded sections. ...with a nodus at the middle of that connecting-thread. . The top-edges of the up-folded sections are horizontally-trimmed on a plane passing through the nodus. . The dial on the bottom-surface is a Horizontal, and the dials on the upturned sections are Vertical-Polar Dials. Hence the name, "Horizontal/Polar Dial". . I prefer Horizontal-Polar, or Universal Horizontal-Polar, or Universal-Box-Polar, as the portable dial for when near-noon accuracy is needed. . When near-noon accuracy is needed, it seems to me that nothing matches the merit of Regiomontanus. . ..except that Universal Box-Polar has easier explanation. But the altitude-formula, on which Regiomontanus is based, is useful in so many sundial applications (declination-lines, altitude-dials, co-ordinate-transmormations for Reclining-Declining Dials), that it's a very sundial-worthwhile explanation. . --------------------- . If universal-ness is desired for a folded-paper flat-dial, then I like the Box-Polar Dial, adjustable for latitude as described above. . ...or Universal Horizontal-Polar, made universal in the same manner. . A folded-paper (with only 1 fold) Universal Disk-Equatorial, as I mentioned in an earlier post, would be another possibility for a universal portable dial, but, as I said, it can be a bit awkward in winter, when it's necessary to read the bottom-surface of the equatorial section. Having tried it, I'd pefer the other designs that I've suggested, which can be read more easily all year. . -------------------- . For a stationary-dial, by some building-methods (such as joining slabs)the Box-Polar Dial might be easier to build than the Cylindrical-Equatorial Dial. . By some building-methods (such as molded Concrete)the Box-Polar doesn't look any easier to build than the Cylindrical-Equatorial. So, then, there'd be no reason to not build the Cylindrical-Equatorial. . 49 M November 25th 2328 UTC . Michael Ossipoff
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