Let me clarify my terminology.
I used "directional" as a category because it is the traditional name for this group and the one used by historians and curators. Frankly, like most of you, I prefer "hour angle." So let's use that for the discussion. I don't think RA is appropriate here, since the sun's RA is very specific for each day of the year.
When I refer to altitude dials or azimuth dials, I am *not* saying that the only thing the dial shows is altitude or azimuth. Any of these projections can be calibrated to give many kinds of information. What I am referring to by the labels is the principal thing that is used to layout the shadow and find the time. Hour-angle sundials all project the sun's hour angle onto some surface, whether the equatorial plane, a horizontal, vertical, or what have you. An altitude dial is calibrated by means of the suns altitude, once the user points it towards the sun at whatever azimuth it happens to be at that moment. The sun's height is the critical thing. In an azimuth dial, the sun's azimuth is the primary focus.
Now, a pin-gnomon dial, or any other nodus suspended/supported above a surface, casts its shadow in accordance with the sun's altitude and azimuth. It seems to me that the azimuth is giving the hour points along "radial" lines (not originating at foot of gnomon), with the position on the line being determined by the sun's declination/altitude at that time of year. However, I would like confirmation of this line of thinking.
At 01:02 PM 1/6/03 +0000, Chris Lusby Taylor wrote:
Equatorial dials, including universal ring dials, are themselves self-orienting, but, rather than combining two distinct projections, they do not use projection. They are the very dials that we see projected in the other cases.
I disagree with this, as the sun's altitude is projected through the pierced gnomon sliding on the bridge onto the equatorial surface. The rotation of the bridge and the rings to bring the spot of light onto the hour scale lines then takes advantage of the sun's azimuth to orient the meridian ring with N-S.
Fer commented on the importance of the type of gnomon: pole-style or nodus-style. I agree that gnomon type--whether a line or point--is important, as is its orientation to a dial surface, but I think that this is subsidiary mathematically to the gnomon's orientation to the celestial sphere or altazimuth coordinates and which primary coordinates are projected onto the surface.
(To this end, I like Chris's description of the classic analemmatic dial as an instrument in which the directions of the projections of the equatorial circle are parallel to the different gnomons. --Incidentally, classic analemmatic sundials were made in an inclinable, folding, pocket-sized form for travellers in the 17th century.)
Augsburg-type refers to a common type of universal equatorial sundial primarily manufactured in Augsburg from about 1675-1825. Makers include Johann Martin, Johann Matthias Willebrand, Lorenz Grassl, and many others.
Keep the comments coming! Sara -
