Yes, the central-gnomon Equatorial dials, with their gnomon parallel to the Earth's axis, and their circular measuring-scale parallel to plane of the equator is educational, because its measurement of Solar Time is completely direct.
And yes, you're quite right: The construction of the Horizontal Dial is easily described in terms of a central-gnomon equatorial (...say, a Disk-Equatorial). Stand a disk-equatorial with its disk resting on the ground and its gnomon (by choosing the right length for it) parallel to the Earth's axis. Draw an east-west line through the point where the disk contacts the ground. Extend the Disk-Equatorial's radial hour-lines (as "rays") to where they meet that east-west line on the ground. Obviously, when the gnomon's shadow is along a radial hour-line of the Disk-Equatorial, it will also go to the point where that ray meets the ground. So draw a line from the ground-contacting end of the gnomon to that point on the east-west line. And then you've constructed a Horizontal Dial. There's a widely-distributed graphical construction instruction that models that construction. The formula: tan A = sin lat tan h ...comes directly from that construction. And yes, as I said in one of my recent posts here, any Vertical or Reclining (but not Declining) flat dial can easily be shown to be a horizontal dial for a different latitude....demonstrable with a globe. Of course the broad category that I described in the paragraph before this one includes the Horizontal Dial, Disk Equatorial, and the Polar Dial as special cases. So yes, all of what you said is true, but it's all surely been out there for a long time. Dialing or dyalling has been studied and described for a long time. I outlined a 5-day set of discussions to explain the construction of the Reclining-Declining Dial. I'll just add that of course it's obvious that there are ways in which a 3D working model of the 3 relevant co-ordinate-systems (Horizontal, Equatorial, and Dial-Plate) could be made and used to construct a Reclining-Declining Dial. I mention that to show that it's possible to truly tell someone that they know of a way that such a dial could be made, even if they haven't heard the 5-day explanation that I suggested. Or, as someone (but probably more than one person) else has suggested one could also start with a Relining-Declining surface, and experimentally, with a plumb-line, and a compass, north-star or pre-made landmark, align a stick (in contact with the surface) so that it's 1) pointing northward, and 2) elevated above the horizontal by an angle equal to your latitude. ...and, from that, build the gnomon. ...and then, using, as reference-dial, any one of the Horizontal, Reclining or Vertical (or Equatorial or Polar) dials described above, hour lines could be drawn on the reclining declining surface where the style-shadow is, when the reference dial says that it's a certain time. That might sound like cheating, but it's a legitimate way that such a dial could be constructed, and for anyone who doesn't want to hear the 5-day explanation, it's way that you could remind someone that they could make such a dial. Michael Ossipoff On Tue, Jul 17, 2018 at 7:13 PM, rodwall1...@gmail.com < rodwall1...@gmail.com> wrote: > Hi all, > > The following is what I think is the best way to describe how sundials > work to kids or anyone. > > > 1st start with the largest sundial in the world. Planet Earth the Master > sundial clock. Stick a vertical stick into the ground at the South pole or > North pole. And describe how the shadow shows the time throughout the day. > Draw the 24 hour lines every 15 deg and that 15 deg x 24 hours = 360 deg > one day. > > Then show how the Equatorial sundial relates to our stick sundial at the > poles. Place it at the South or North pole. And show that the Equatorial > sundial style edge is parallel with the stick and the axis of the Earth. > And that the hour lines are the same every 15 deg. And that it will keep > the same time. > > Then place the Equatorial sundial anywhere on earth. And show that the > sundial is geared to Earth the largest sundial in the world (the Master > sundial clock). Therefore it will keep the same time. Show how the sundial > time markings relate to your local time. And that the style edge of the > sundial must be parallel with the axis of the earth and parallel with the > vertical stick at the poles. And that at night time the sundial is in the > shadow of Earth. > > Then place a horizontal sundial at the same location. And describe that > the style edge is also placed parallel with the stick and the axis of the > Earth. And how the hour lines are projected every 15 deg from the > horizontal sundial style. That is to place the style edge of the equatorial > sundial onto the horizontal sundial style edge and use it to project the > hour points onto the horizontal base of the horizontal sundial. Then draw > the hour lines on the horizontal sundial. Then show the direction the > horizontal sundial faces if in the Southern hemisphere or Northern > hemisphere. To ensure that the Style edge is parallel with the axis of the > Earth and stick. > > Then go through the same process as you did for the horizontal sundial but > with a vertical sundial on a wall. And show that it must face North towards > the sun if in the southern hemisphere and face South for the northern > hemisphere. Yes I live in sunny Australia in the southern hemisphere. > > Then show how the angle of the style edge relates to the latitude of the > location of the sundial. To make the style edge parallel with the stick and > axis of the Earth. > > Depending on how far you want to go. Describe how a horizontal sundial > that is not designed for the latitude of the location you are at. Can be > corrected if a block is placed under the dial to make the style edge > parallel with the axis of the Earth and the stick. > > Describe how longitude relates to your location. And that the longitude > time zones are every 15 deg. 15 deg x 24 hours = 360 deg one day. > > One way to describe the above is to use a globe of the world or a large > beach ball. With cardboard cutouts for sundials. And a lamp (sun) to make > the shadows. Young kids and some adults learn better when learning in the > sand pit (concrete learning) rather that just using symbolic words > (symbolic learning). > > That is how I explain it. > > If anyone wants to publish the above. Please do and let them know where it > came from. > > Have fun, > > Roderick Wall > Sunny Australia. > > >
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