dear John
there is a precise theoretical procedure to relocate a sundial so that
it works correctly in a new location (for the hour lines).
In the most general case, the sundial must be placed with a new
orientation so that the style keeps the polar orientation in the new
location (thinking of the stylus and dial as one whole).
This condition provides for many orientations, all the orientations
obtained by rotating the dial around the polar stylus.
The difference caused by these rotations is the meridian to wich the
time marked will refere, that is, as well as orienting the polar style
correctly, a rotation around the axis may be necessary for the marked
time system to be correct (local sun time, time-zone sun time).
It seems a little bit complicated, indeed it is, but it can be solved.
If the new location is very close there are not all these complications,
you have only to keep the same orientation.
If the difference are few degrees in declination of the wall, you can
place the sundial not parallel to the wall (keeping polar the stylus),
otherwise, as you write, you have to accept an error.
The error is not constant at the same time, it also changes with the
declination of the sun, that is, it is seasonal.
The answer to your question is a three-dimensional graph, with time and
declination of the sun on x and y axes and the error on the z axis.
The error doesn't depend on latitude but on the angle between the polar
axis and the non-polar stylus.
Not last, there is a consideration similar to that of Lewis Carroll
about the stopped clocks that strike the right time twice a day:
a non-polar stylus, whatever its orientation, always shows the correct
time once a day, when the sun is in the hourly plane that contains the
non-polar stylus and the polar axis. This plane relates to two times 12
hours apart.
In the other times the error occurs according to the declination of the
sun, cancelling itself every 12 hours, whit the max error about halfway.
The paradox would therefore be that accepting a little approximation in
the direction of the stylus is not important. This is the reason why
even in front of a wrong sundial there are those who can say that they
saw it strike the right time.
If it were not a paradox it would be the end of gnomonics :-(
I think that few degrees of error in the direction of the stylus (2-3°)
might be acceptable, but it also depends on the size of the sundial and
therefore on the comparison between the accuracy in the reading and the
error due to the non-polar stylus.
ciao Fabio
Il 08/11/2021 14:38, John Foad ha scritto:
If a vertical dial is relocated and now faces a few degrees east or
west of its designed declination, you might expect it to run a few
minutes slow or fast. Has anyone ever tabulated the greatest error,
and at what times and dates it occurs? And does it make sense to
think about the average error? Clearly the errors depend on the
latitude and the design declination, but for starters they could be
tabulated just for a direct south dial at 52.5 degrees N, and for a
location move of 1, 2 and 5 degrees either way. As the gnomon is no
longer polar-pointing I imagine the maths is a bit hairy.
Best wishes,
John Foad
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--
Fabio Savian
fabio.sav...@nonvedolora.it
www.nonvedolora.eu
Paderno Dugnano, Milano, Italy
45° 34' 9'' N, 9° 9' 54'' E, UTC +1 (DST +2)
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