There are several different issues:
1. The legibility of symbols on the dial is primarily based upon human
visual acuity and the distance from the observer to the dial. This was
Ross Caldwell's initial question.
2. The visibility of a line on the dial is another matter, with a
high-contrast line (for example a wire against the sky) 0.5 arc second in
width being visible under good conditions (Hect and Mintz, J. gen. Physiol,
vol. 22, pp. 593-612, 1939, for those who wish to look up the original
article).
3. The visibility of the shadow of a cable gnomen is based more upon the
solar angular diameter, the diameter of the cable and the distance of the
cable from the dial. This was John Carmichael's question. Bill Gottesman
is quite correct that the angular width of the penumbra is usually
determining, although the location of the penumbra can usually be
determined to a fraction of its width. Note that the distance from the
gnomen to the dial is usually different from the distance from the observer
to the dial.
4. The determination of the position of the edge of the shadow of a solid
gnomen depends primarily upon the solar angular diameter and the distance
from the edge to the dial. If the angular size of the penumbra were less
than human vernier acuity (the precision to which verniers can be read)
then the latter might be limiting; this is on the order of 5 to 12 arc seconds.
5. If the dial is significantly tilted with respect to the line of sight
then a cosine correction factor may be appropriate.
Gordon
At 12:17 PM 2/11/00 -0500, [EMAIL PROTECTED] wrote:
Sorry to be a kill-joy, but I fail to see the utility of scribing hour lines
near the limit of human resolution, when the shadow's edge cast by a solid
(non-wire) gnomon is blurred by the 0.5 degree width of the sun.
Bill Gottesman
Burlington, VT, USA
lat 44.47583, long -73.202581
Gordon Uber [EMAIL PROTECTED] San Diego, California USA
Webmaster: Clocks and Time: http://www.ubr.com/clocks
