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Re: Biruni and the radius of the Earth by dip
From: John Huth
Date: 2011 Jan 4, 18:23 -0500
From: John Huth
Date: 2011 Jan 4, 18:23 -0500
In this article, too, the author goes to some length to justify that al-Biruni averaged 10 measurements and waited for an exceedingly clear day - not that the clarity implies no refraction correction.
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Keeping up with the grind
There's also what appears to be an error in the value of sines that kick things in the right direction.
Evidently al-Biruni was trying to confirm a measurement done by two teams commissioned by Sultan Mahmud derived 56 1/4 miles as one degree by using a different technique. Mahmud's is the more standard labor intensive technique of marching over a long distance.
Some writers, like the author of the article on Geodesy suggest that al-Biruni gave up and just adopted Mahmud's value as correct. Others, like the author of this paper suggest that the averaged measurements and the clear day gave him a value of 34 arc minutes, but that the precision was only good to about 20%.
All agree that we don't know his measuring device. All agree that he didn't account for refraction, although some simply skip that part. In the Wikipedia article you posted, the author suggests a large astrolabe, although I found myself drawn more to a hydraulic solution to get enough precision.
The Mahmud value is also surprisingly "on" - I don't know what to make of that one. The problem, of course is that you need a clear case for the precision of a measurement. Knowing that a measurement is spot on in retrospect of the modern era didn't help someone in the 16th or 17th century.
On Tue, Jan 4, 2011 at 4:48 PM, George Huxtable <george@hux.me.uk> wrote:
Since I posted the following, in the early hours of this morning, there
have been three postings on the Biruni topic, none of them referring to
that text.
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I think I have found what John Huth is seeking, though I haven't really
read it yet. It's at-
http://www.jscimath.org/uploads/J2010145AG.pdf?CFID=1980504&CFTOKEN=51765461&jsessionid=84303618f42d5fc6af37543e5fa6358265d7
It's ref 37 in the Wikipedia page on Biruni,
Gomez, A. G. (2010) 'Biruni's Measurement of the Earth', Journal of
Scientific and Mathematical Research.
I've no idea whether it's worthwhile or not.
=======================
That recent paper deals with the question of refraction, and claims to have
identified the mountain used for the observation, in the Himalayan
foothills South of Rawalpindi, and provides a profile of the plain below
it, to the South, between the Jhelum and Chenab rivers, which was claimed
to suffice in place of a sea-horizon.
There are several curiosities, including the notion that with an astrolabe,
one might measure a dip of 34' to the nearest minute. All astrolabes that I
have seen have been divided to whole degrees, no finer, and the sighting
and levelling arrangements are remarkably crude. It seems clear that any
similarity between the true radius of the Earth and Biruni's result can
only have been accidental.
I suggest that anyone making pronouncements about Biruni's procedure should
first take a look at the Gomez paper.
George.
contact George Huxtable, at george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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Keeping up with the grind
