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
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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
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https://lists.uni-koeln.de/mailman/listinfo/sundial
