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Hi
Baruffi, I also think that your assertion is not
correct: I try to make some consideration.
In the calculations of a sundial with the
classical methods all adopt, from a long time, a schematic and simplified model
of the sky and of the motion of the Sun.
As Fer de Vries has already written, today we could use more precise formulas
and more complex methods and consider all the parameters that affect the lines drawn from the shadow in
a sundial. In ancient times this was not possible and also
when it became feasible (already with the Arabs after 900 AD) the thing was not
even considered, having no
importance a great precision.
By the way the formula written by Fer, that
gives the length of half the period of light, was already known and used as a
geometric construction since the
beginning of our era and it was known and used in trigonometric form till the time of the Arabs (about 900-1000) :
obviously they did not use our mathematical notation that was introduced only
after 1600. A proof of this are the numerous tables
calculated with trigonometric formulas that were used from the Islamic
astronomers for the calculations of
the sundials. In the simplified model we have : -
the Sun reduced to a
point -
the declination of the
Sun constant during the whole day (otherwise we would not have nor straight lines,
nor hyperbola) -
the declination of the
Sun =0 deg on the Equinoxes
-
the length of the
period of light = 12 hours on the Equinoxes (Italic, Babylonian, temporary or
solar hours ) -
the effect of the
refraction is not considered (greater than that of the Suns semi diameter) -
dawn and sunset are
defined as those instants in which the punctiform Sun crosses the ideal horizon
(without considering the effect of the depression of the horizon caused by the
height of the place). In astronomy today, dawn and sunset are defined as those
instants in which the zenith distance of the center of the solar disk = 90deg 50
' (Explanatory Supplement to the Astronomical Almanac - pag. 32) When we think to our ancient
predecessors we don't have to get confused: even if in the practice the sunset
was, as today, the instant of the disappearance of the solar disk , for the
students of the sky (astronomers or astrologers) it was the instant in which the
ideal sun goes down under of the ideal horizon. For instance on 20/3/2005 (Spring
Equinox): - for the calculation of a sundial the Sun
rises at 6h of solar time and the Suns declination =
0deg - if we consider only the refraction it rises
at 5h 57m 17s
- if we consider also the upper edge of the
solar disk it rises at 5h 55m 47s
- Moreover the Suns declination changes from -6' 30.8" at dawn to +5' 29.4"
at sunset We can see that the ancient used this
simplified model observing a whatever sundial with solar, Italic and Babylonian hour lines. In these sundials the lines of the different
systems always pass through the same points on the equinoctial line: the line of
hour H of solar time met that of
Babylonian hour H-6 and that of
Italic hour H+6 (f.i. 11h of solar
time, 5h Babylonian, and 17 Italic)
If the beginning of the Italic hours were in the instant in which we see the
superior edge of the Sun disappear under the horizon then, on the days of the
Equinoxes the Italic hour 0h would begin
at 18h 4m of solar time
(around) and the Babylonian hour 0h would begin at 5h 56m: for this reason the lines of the
different systems of hours would not cross on the equinoctial line. Moreover the duration of the period of light
would be of around 12h 9m and therefore 1 temporary hour would be longer than 1
solar hour. All this is not observable in any of the
ancient sundials.
Gianni Ferrari P.S. I had sent this message yesterday, but it
has not arrived :-
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