Dear Friends Don't forget the beautiful Missal of St Leofric 10-11th Century for an elegant but simple shadow length table see http://image.ox.ac.uk/show?collection=bodleian&manuscript=msbodl579 and find folio 58 recto
Does anyone know if Bede's Table is available in manuscript image form anywhere on the web (plus a translation...!)? Best regards Kevin Karney Freedom Cottage, Llandogo, Monmouth NP25 4TP, Wales, UK 51° 44' N 2° 41' W Zone 0 + 44 1594 530 595 On 9 Mar 2011, at 15:03, Schechner, Sara wrote: > 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 | sche...@fas.harvard.edu > http://www.fas.harvard.edu/~hsdept/chsi.html > > > > From: sundial-boun...@uni-koeln.de [mailto:sundial-boun...@uni-koeln.de] 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 <billgottes...@comcast.net> wrote: > > From: Bill Gottesman <billgottes...@comcast.net> > Subject: A 14th century sundial question from France. > To: "Sundial Mailing List" <sund...@rrz.uni-koeln.de> > 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 >
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