R: R:

[Ing. Lucio Baruffi]

Hi Gianni, I didn't hope in your intervention anymore in this debate, when has arrived to me your e-mail , that provides me same starting points to sustain and to clarify better my thesis. The Sun, gives its apparent dimensions, not always can be considered punctiform as the stars; the determination of the sunset and the sunrise, understood as disappearance or apparition of the solar disk, is one of these cases. Therefore there are not news that the reference to the center of the Sun is antecedent to 900 AD, while the solar clocks of which we speak go up again to some thousand of years before. To this long period we have to look if we want to follow to the antiquity, since these clocks no more serve us for practical needs, but as suggestive ornaments. You affirm: "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,.." it is what I assert . As for instance Jean Meeus, astronomer well known to many of us, for the calculation of the hourly angle to the time of the sunset it points out the formula inserted in my preceding e-mail, which formula refers to the superior edge and also keeps in mind the refraction. In the effemeridis the instant of the sunset and the to sunrise is reported to the superior limb of the Sun. Insofar all those that, to calculate these types of solar clock, use the data of the effemeridis, refer to the superior edge and if the hourly lines don't meet on the equinoctiale line those corresponding of the solar time as in the graphics based on the center of the Sun, no matter because this last is an empirical system. Obviously each can choose the method that prefers and mine are considerations of method and currently of any practical importance, because the solar clocks, as it justly observes Fer de Vries, arn't used in our daily live. A dear regard, Lucio.   -----Messaggio originale----- Da: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]Per conto di Gianni Ferrari Inviato: martedì 28 settembre 2004 19.26 A: LISTA INGLESE Oggetto: R:R: 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 Sun’s  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 Sun’s 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 Sun’s 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  :- (