I had exactly the same thought as John-that this was a table of shadow lengths in the form that Bede gives in the 7th century. Sara
Sara J. Schechner, Ph.D. David P. Wheatland Curator of the Collection of Historical Scientific Instruments Department of the History of Science, Harvard University Science Center 251c, 1 Oxford Street, Cambridge, MA 02138 Tel: 617-496-9542 | Fax: 617-496-5932 | [email protected] http://www.fas.harvard.edu/~hsdept/chsi.html From: [email protected] [mailto:[email protected]] On Behalf Of JOHN DAVIS Sent: Wednesday, March 09, 2011 5:13 AM To: Sundial Mailing List; Bill Gottesman Subject: Re: A 14th century sundial question from France. Hi Bill (and other dialling colleagues), The data that you show looks very similar to the Venerable Bede's shadow length tables (though the values are slightly different). This gives the length of a person's shadow on the assumption that their height is equal to six of their own feet (tall people generally have big feet!). But the hours are probably not the modern equal ones. This topic will be discussed in some detail in the forthcoming June issue of the BSS Bulletin. A reason for the inaccuracies will be proposed, together with a rather more accurate version of the same table, to be found in an Anglo-Saxon manuscript. Regards, John --------------------------------------------------------------------------------- Dr J Davis Flowton Dials --- On Wed, 9/3/11, Bill Gottesman <[email protected]<mailto:[email protected]>> wrote: From: Bill Gottesman <[email protected]<mailto:[email protected]>> Subject: A 14th century sundial question from France. To: "Sundial Mailing List" <[email protected]<mailto:[email protected]>> Date: Wednesday, 9 March, 2011, 1:06 Richard Kremer, the Dartmouth physics professor who brought the ~1773 Dartmouth Sundial to display at the NASS convention this past summer, asked me the following question. I have done a bit of modelling on it, and have not been able to supply a satisfactory answer. Is anyone interested in offering any insight? My hunch is that the astronomer who wrote this guessed at many of these numbers, and that they will be estimates at best for whatever model they are based on. I have tried to fit them to antique, equal, and Babylonian hours, without success. In 1320, the equinoxes occured around March and Sept 14 by the Julian Calendar, as best I can tell, and that doesn't seem to help any. -Bill --- I've got a sundial geometry question for you and presume that either you, or someone you know, can sort it out for me. A colleague has found a table of shadow lengths in a medieval astronomical table (about 1320 in Paris). The table gives six sets of lengths, for 2-month intervals, and clearly refers to some kind of gnomon that is casting the shadows. The manuscript containing this table of shadow lengths appears in a manuscript written by Paris around 1320 by John of Murs, a leading Parisian astronomer. I don't know whether Murs himself composed the table or whether he found it in some other source. The question is, what kind of dial is this. A simple vertical gnomon on a horizontal dial does not fit the data, which I give below. Dec-Jan hour 1 27 feet hour 2 17 feet hour 3 13 feet hour 4 10 feet hour 5 8 feet hour 6 [i.e., noon] 7 feet Nov-Feb 1 26 2 16 3 12 4 9 5 7 6 6 Oct-Mar 1 25 2 15 3 11 4 8 5 6 6 5 Sept-Apr 1 24 2 14 3 10 4 7 5 5 6 4 Aug-May 1 23 2 13 3 9 4 6 5 4 6 3 Jul-Jun 1 22 2 12 3 8 4 5 5 3 6 2 Note that in each set, the shadow lengths decrease in identical intervals (-10, -4, -3, -2, -1). This might suggest that the table is generated by some rule of thumb and not by exact geometrical calculation, for by first principles I would not expect these same decreasing intervals to be found in all six sets! I started playing with the noon shadow lengths at the solstices, looking for a gnomon arrangement that yields equal lengths of the gnomon for shadow lengths of 7 (Dec) and 2 (Jun) units. If you assume the dial is horizontal and you tilt the gnomon toward the north by 55 degs, my math shows that you get a gnomon length of 2.16 units. I assume that Paris latitude is 49 degs and the obliquity of the ecliptic is 23.5 degs (commonly used in middle ages). I'm too lazy to figure out the shadow lengths for the other hours of the day with a slanted gnomon, and presume that you have software that can easily do that. Would you be willing to play around a bit with the above lengths and see if you can determine what gnomon arrangement might yield these data? Perhaps the dial is vertical rather than horizontal? In any case, the data are symmetrical, so the gnomon must be in the plane of the meridian. Knowing that you like puzzles, I thought I'd pass this one on to you. If you don't have time for it, don't worry. This is not the most important problem currently facing the history of astronomy! Best, Rich --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
--------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
