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Re: Biruni and the radius of the Earth by dip
From: John Huth
Date: 2011 Jan 4, 17:17 -0500
From: John Huth
Date: 2011 Jan 4, 17:17 -0500
George -
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Keeping up with the grind
I did print out and read this article. What I was struggling with was the more profound claim that it was the best measurement until the 18th century. That was occupying more of my time today.
In this article, he does comment on the effect of refraction at the very end and says that the measurement was correct to about 20% or so. I think the quoted measurement of dip was 34 arc minutes, and suggests that al-Biruni was lucky, as the last significant digit could've been different, and thrown the radius off by a lot. The analogy with Eratosthenes is apt, with the Egyptian/Greek stade, since the quote of al-Biruni's accuracy was two significant figures in arc minutes. Eratosthenes distance was 5000 stade.
It's pretty clear that a) al-Biruni didn't do a refraction correction and b) probably had at best a few arc minutes accuracy. This article seems clearer than the Razvi article, which quotes a paper that he found in 1959 and he goes to far too many significant figures, as opposed to the Masudic canon, which is in the paper you posted. We don't know what instrument al-Biruni used.
20%, as suggested by the article seems plausible, but still pretty good - so I don't really have a problem with this article - I think the more profound claim.
So based on this paper, the History of Cartography article I read and a few other sources, I think that he had a decent technique that's interesting, but one can't push the precision too far. It also appears that this value competed with other contemporary values in measurements of a degree of latitude. The main point is that it doesn't require heroic efforts to measure long distances precisely. The quotation in Wikipedia seems to impart more precision than is warranted, but this paper seems right.
John
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.
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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
