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    Re: Biruni and the radius of the Earth by dip
    From: John Huth
    Date: 2011 Jan 7, 11:26 -0500

     George (et al) - 

    Frank presents a fairly good summary of our discussion.    I'll add a bit of background now that I've done some reading on the history of this.   The source I trust the most is The History of Cartography - Vol. 2 Book 1, in a chapter on Islamic Geodesy - but I've confirmed this from some other sources. 

    The historical background is a bit sketchy, but in the 10th century Caliph al-Ma'mun directed a survey that used a relatively long baseline, traveling 19 farsakhs (1 farsakh = 3 miles approx) from Mosul and 43 from Samarra.   They made a series of astronomical measurements and presumably had some tight control on the baseline.   There is some confusion about whether they measured 56 or 56 2/3 Arab miles to the degree, but that was taken as the "state of the art" of the era. This was reported by an astronomer named al-Farghani and I believe this is relatively well known.

    al-Biruni wanted to do the equivalent survey in the 11th century, but evidently could not get sufficient support to do this manpower intensive activity.    He was detained near a fort in the Punjab and was trying to figure out a more clever way of doing this without a large amount of support, and hit on the concept of using the dip angle.     

    In al-Biruni's account, we do not know the instruments he used, hence my curiosity about whether a water trough would be sufficient for the angular accuracy.   He measured the height of the mountain from two observation points.   He gives the height of the mountain as 652 1/20 cubits, and quotes a dip angle of 34 arc-minutes, although it appears he artificially lowered this from 35 arc-minutes.   

    As we've discussed, and others as well, he didn't employ any correction for refraction and one could indeed have a flat-Earth.   I wonder what would've happened if he derived a concave Earth.  I am a bit curious as to what atmospheric conditions would be required to obtain a flat or concave Earth from a mountain 500 m high, using dip and no correction.   

    As far as I can tell, al-Biruni's measurement didn't "stick" in any historical sense, but the al-Farghani measurement did.  

    The modern version of al-Biruni's measurement seems to arise from this paper by Samad Rizvi in 1973 and this appears to be where it gathers steam over the last few decades.   

    Mercier's article on Geodesy tackles this reasonably well.   He points out that a "standard" refractive effect would take the 34 arc-minutes down to 29, but he's also careful to point out that al-Biruni might have fabricated the number out of whole cloth to agree with the al-Farghani measurement, or come close to it, in any case.   There also appears to be an error in his use of sines that compound the problem.   

    In any case, it appears to be a purely accidental measurement, although I think Mercier's point that al-Biruni *wanted* to reproduce the earlier measurement is plausible, and he just happened to hit the mark.   In any case, it has no historical significance as this measurement didn't get any "legs", unlike the al-Farhani one.   

    In terms of the paper you mentioned in Wikipedia, I don't think a really big astrolabe would've cut it, so that's why I was wondering about whether a water trough would work.   

    I *have* seen water used in a surprising application.   Since you're a physicist, you probably have heard of the Stanford Linear Collider.   I once took a tour of the tunnels, which are two arcs used to bend the electron and positron beams.   The big issue was the alignment of magnets in the two funny shaped arcs.    When I was walking through the tunnel, I saw some vessels of water with tubes leading away to the other arcs.   They were using this technique to align their magnets!   This isn't speculation, one of the accelerator physicists pointed this out to me.


    John H. 

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