HI Roger,
Thank you for sending the René Rohr reference. I wish I had had it when I was
writing my article for the compendium, which on re-reading I find to be pretty
incoherent. René Rohr’s version is more or less what I should have written up
to the point where he explains the latitude mismatch. I think René Rohr (and
others) are wrong about the dial having been correctly made for somewhere else
and then moved. I have a copy of volume XXX of the archeological report on
the excavation which covers the two sundials found at the site. The report
also includes the speculation, repeated by others, that it was designed for
India or Syene, even though the report notes that the dial is made from
limestone similar to other carved items, such as pillars, found at the site.
My own contribution to the Ai Khanum discussion is an admittedly speculative
theory that the latitude mismatch could have resulted from a simple
construction mistake. I start with the assumption that the astronomer or
mathematician who designed the dial specifications would not be the person who
would do the physical construction including stone cutting. I tried to imagine
how one might go from a theoretical specification to actually marking lines out
on a piece of stone at a time when most of the measuring tools and methods we
might use did not exist or were not widely available. I concluded that the
specification of the angles would likely have been stated in terms of ratios
which would then have been realized by making right triangle templates to do
the physical layout. All the measurements needed for the physical
construction of this dial could have been specified by two triangles: one
representing the earth’s obliquity and the other the local latitude. My
hypothesis is that the obliquity triangle was mistakenly used in place of the
latitude triangle. It is therefore not a random coincidence that the temporal
lines which would be correct for a latitude of about 23.7 degrees is also the
same as the earth’s obliquity at the time.
But since my knowledge of paleo-mathematics is even weaker than my knowledge of
stone-cutting techniques, I would be interested in the opinions of those who
know more about the period whether my “right triangle theory” is plausible.
As Karlheinz has already pointed out, the Arachne of the Amphiareion is, of
course, equatorial and not horizontal as I originally said.
Jack Aubert
From: Roger Bailey [mailto:[email protected]]
Sent: Monday, August 03, 2015 8:13 PM
To: Jack Aubert; [email protected]; Sasch Stephens
Subject: Re: Temporal Hours
Hi Jack,
While following a lead based on Sasch Stevens display at the conference, I came
across an interesting article on the Al Khanum dial by Googling "Alexander the
Great sundial". This search found this article: "A Unique Greek Sundial
Recently Discovered in Central Asia" by Rene Rohr in 1980 in the JRASC. The
article describes the work at Al Khanum by Paul Bernard. See
http://adsabs.harvard.edu/full/1980JRASC..74..271R Their conclusion is the same
as yours, the dial is a an equatorial with a polar gnomon but the lines show
temporal hours rather that straightforward equal hours.
Regards, Roger
From: Jack Aubert <mailto:[email protected]>
Sent: Sunday, August 02, 2015 6:55 PM
To: [email protected] ; [email protected] ; [email protected] ;
[email protected]
Subject: RE: Temporal Hours
I assume that you are referring to the Arachne of the Amphiareion. I have a
photocopy of your article on that dial, which was reconstructed from fragments,
describing a (very old) horizontal dial with equal hours.
Another atypical dial: The Ai Khanum dial found in the ruins of Alexandria on
the Oxus (in modern Afghanistan) that dates from approximately 145 BC is an
example of a polar-oriented gnomon with unequal hours. This dial is
interesting for several reasons, in particular the fact that while it
“naturally” told equal hours using the line-shadow of the gnomon, the
constructor carefully incised lines to read unequal hours using the gnomon tip.
(It was done incorrectly for its latitude, but that’s another story.)
However, both these dials are quite exceptional. My general impression from
what I have been able to read is that equal hours were used by astronomers and
astrologers. While there is at least one example of a horizontal dial that
uses equal hours and at least one example of a polar gnomon using temporal
hours, people generally wanted their time in temporal hours so the vast
majority of surviving dials prior to the Ibn al-Shatir dial used temporal
hours.
Jack Aubert
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