John
Actually the length of an arc of longitude at a
specific latitude is proportional to the radius
of the parallel for that latitude .This radius is
equal to the radius of Earth x cos(latitude). It
is the same for the length of one degree of
longitude. So at your latitude (32°13'18") the
length of one degree of longitude is 111,32 x
0,846 = 94,18 km. So one second of longitude is
26 m.
As for the accuracy of coordinates, especially
latitude, to be used for designing sundials I
think the minute of arc, or half the minute, is
quite enough. A sundial is not really different
1852 m north or south, or even more 900 m north
or south. In theory it is different, but actually
it is not. I don't want to say that dialling is
not an exact science, but diallers have to face
actual world : how to be sure a wall is perfectly
vertical ? Is it possible to measure the bearing
of a vertical wall with an arc second accuracy ?
Generally the minute of arc is not so bad. Hours
lines have to be drawn with some width to be
seen. Etc...It depends also on the size of the
dial. For large dials it should be necessary to
find the latitude with an accuracy of, say, 10
arc seconds.
Afterwards you still can label the dial with the
exact coordinates of the place accurate to the
second of arc. But, then, to be rigourous, you
should mention the geodetic datum ( WGS84, NAD27
for the USA, ED50 for Europe, etc..), because the
same place has slightly different coordinates
when expressed in different geodetic datum; the
difference concerns the seconds of arc. People
using GPS receivers know that problem especially
at sea.
Regards
Jean-Paul Cornec
