|
Dear
Baruffi,
obviously, as also you say, each of us can calculate his own sundials
with the method and the formulas that more he prefers and loves. It is
therefore possible to consider the instant of the sunset as defined by modern
astronomers and to use both the
upper bound of the solar disk and
the refraction as established in the Explanatory Supplement to the Astronomical
Almanac or in the formula of Meeus (correct with 0.01454=sen(50 ') and not with
0.1454 :-) ) Different it is however the case of the ancients: I don't
think that it is possible, even if it seems opportune and natural, to make the
hypothesis that you do and to suppose that they used the upper bound of the Sun to
calculate the instant of dawn from which to begin to mark the temporary hours
in the sundials.
Obviously also they saw and knew that the Sun disappears
when its superior edge goes under the horizon, but I do not know any proof that
they used this instant as the beginning of the hours in their drawings and
plans of sundials.
The
fact that, for ignorance or for greater facility of execution, they used a more
simplified model of the reality, can be seen also in all the Roman
sundials that were produced ( we think) following the methods of the analemma
(or projection of the celestial vault), described very clearly by Vitruvius (De
Architectura, liber IX)
Vitruvius in all his description makes reference to the
Sun as to a point, he speaks of single rays that pass for the center,
etc.. He
also uses ulterior geometric
simplification supposing the ecliptic inclination = 24deg = 360/15, whose
construction can be found in the In my
opinion is not true what you
assert "there is no proof of the use of
the center of the Sun before 900", but it is exactly the contrary , that is
"it doesn't exist any proof that the sundials from around 300 BC,
till around For
what I know, also today no one calculates the sundials according to your
direction. Some
times, for very great sundials,
the refraction is considered, but
in all the other cases, either for simplicity of shape, either for love of the
straight lines, and certainly not for the difficulty in the calculations, all
take the Sun as puntiform.
The
error is very small and comparable to that
caused inevitably by the
fact that the year is long not a whole number of days, for which in a same day
in following years the declination of the Sun changes slightly. Obviously in the Ephemerides we find the exact instants
of the dawn and of the sunset of the Sun and if someone (?) uses these
values to plan a sundial with ancient hours (Temporary, Italic,
Babylonian) he doesn't use the
method of our predecessors and he will not obtain courses of the lines as
those of the ancient sundials that he wants to reproduce. I
don't know anyone that acts in this way, when the formula already written by Fer
de Vries is very simple, while the instants given in the almanacs are in
Standard and not in Solar Time and moreover they are never given for the place
that interests us, since this values change with the latitude. A regard Gianni Ferrari
44° 39' N 10° 55' E
|
