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    Re: Two reckonings
    From: George Huxtable
    Date: 2011 Jan 4, 00:27 -0000

    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.
    
    George.
    
    contact George Huxtable, at george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message -----
    From: "Apache Runner" 
    To: 
    Sent: Monday, January 03, 2011 8:04 PM
    Subject: [NavList] Re: Two reckonings
    
    
    | George -
    |
    | That's partly why I asked.   I can find very little about al-Biruni's
    | measurement, so it could be modern exaggeration.   I'm assuming that he
    left
    | some material, but it's difficult to find any translation or material
    that
    | goes beyond the superficial.   I did a Mathematica simulation of what he
    | would've seen, assuming that it was one of two mountains in the Punjab
    and
    | the effect was very small.    I went so far as to imagine giving this as
    an
    | assignment to my students, but when I realized that it would be difficult
    to
    | get any accuracy, I scrapped the idea.   I couldn't imagine how one could
    do
    | this with the tools he had available.   He was a smart guy, so I could
    see
    | that he could create something better than an astrolabe, but I'm not sure
    | what.
    |
    | It's possible Sarton's work has some material on this.
    |
    | Best,
    |
    | John H.
    |
    |
    | On Mon, Jan 3, 2011 at 2:53 PM, George Huxtable  wrote:
    |
    | > John Huth wrote-
    | >
    | > | George -
    | > |
    | > | That's truly fascinating, but I guess I shouldn't be surprised by the
    | > | problems of standards.   What surprised me the most in your post is
    that
    | > the
    | > | circumference of the Earth  was in dispute so late in the game.
    | > |
    | > | As I recall Abu Rayhan Biruni had an exceedingly accurate measurement
    of
    | > the
    | > | circumference of the Earth way back in 1000 AD.   He used a dip-angle
    | > | technique of all things.   Perhaps it was not widely accepted.   I'm
    | > | actually interested in al-Biruni's technique, as I'm having
    difficulties
    | > | tracking this down.   It's widely known that he used dip angle from a
    | > | mountain in the Punjab, but the precise technique is something I've
    found
    | > | elusive.  If I were to do this measurement, I'd probably use a trough
    of
    | > | water for my horizontal, but then I'd also have to have a fairly well
    | > | calibrated device to sight the dip angle.    If anyone out there
    knows
    | > about
    | > | this measurement, I'd be grateful for the details.
    | > |
    | > | I'm assuming that Snell and Gunter did a more standard
    | > astronomical/survey
    | > | measurement.
    | >
    | > ================
    | >
    | > To deal with John's last point first, it was Snell's measurement in
    | > Holland, and Norwood's from London to York, that were important.
    Gunter's
    | > role was more as a teacher and a persuader.
    | >
    | > I hadn't come across Abu Rayhan Biruni, except as a name, but since
    reading
    | > your post I've Googled him. It strikes me that to achieve sufficiently
    | > precise measurements of the small angles involved, to reach the claimed
    | > precision for the Earth's radius (except accidentally) an astrolabe ,
    which
    | > won't measure such angles better than to a quarter of a degree or so,
    is
    | > insufficiently precise. So I'm a bit sceptical about that article.
    | >
    | > We have to take account of another possibilty. Biruni's observation, in
    the
    | > end, depended on some baseline, which may have been just paced-out or
    | > checked with some measuring cord, in what was called "cubits". Were
    | > standards of linear measurement, in the 11th century Muslim world, like
    | > they were in the West, to the 18th century and beyond, when each state,
    and
    | > often each city within that state, had its own set of weights and
    measures,
    | > quite incompatible with everyone else's, and altering from one era to
    | > another? The French, Spanish, German, Dutch, and English leagues
    differed,
    | > considerably. How well is al-Biruni's cubit independently known today,
    in
    | > terms of modern metres? I ask, because it could be that the al-Biruni
    | > conclusion, in terms of cubits per degree of latitude, may have been
    the
    | > basis for modern scholars to assess the true length, in metres, of the
    | > cubit he used. In which case, his conformity with  modern values of
    | > Earth-radius would have been a self-fulfilling circular argument.
    | >
    | > Let me make it clear that I have no knowledge, at all, about whether
    such a
    | > state of affairs actually existed. But it might have done.
    | >
    | > Similar problems arose with Eratosthenes' measurement, between
    Alexandia
    | > and Syene, around 200 BC, in that we know just what he did. We know
    what he
    | > measured, it stades, and the angle it subtended at the Earth's centre,
    but
    | > we don't know what value of the stadion he used, as they came in
    different
    | > local varieties.
    | >
    | > George.
    | >
    | > contact George Huxtable, at  george{at}hux.me.uk
    | > or at +44 1865 820222 (from UK, 01865 820222)
    | > or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    | >
    | > | On Sun, Jan 2, 2011 at 7:26 PM, George Huxtable 
    | > wrote:
    | > |
    | > | > John Huth wrote-
    | > | >
    | > | > "The local curator of the Museum of Historical Scientific
    Instruments
    | > told
    | > | > me that the sand-glasses were 28 or 29 seconds, rather than 30.
    Could
    | > | > this be to also create an in-built over-estimate of distance run?
    | > | >
    | > | > I guess this doesn't completely cover problems like what Cook
    | > encountered.
    | > | >
    | > | > ============
    | > | >
    | > | > John is operning up an intriguing can o'worms here. This matter
    became
    | > very
    | > | > complex.
    | > | >
    | > | > The English Log, which came into use in the 16th century, was the
    first
    | > | > decent way of assessing a ship's speed in numerical terms. And
    mariners
    | > | > came to realise that the answers it was giving them were failing to
    | > | > correspond with their observed latitude changes, even in simple
    | > North-South
    | > | > travel.
    | > | >
    | > | > The reason was, mainly, a misunderstanding of the size of the
    Earth,
    | > and
    | > | > therefore the length of an arc-minute of latitude, expressed in
    feet.
    | > Over
    | > | > the 17th century, as a result of the work of Snell (same man as in
    | > Snell's
    | > | > law) in Holland, and Gunter and particularly Norwood in England,
    the
    | > | > assessed sea-mile increased from 5000 feet to 6000 feet and then
    6120
    | > feet.
    | > | > Mariners had to adjust their logs accordingly. It wasn't a trivial
    | > | > business, increasing the spacing between the well-embedded knots
    along
    | > 600
    | > | > feet or so of line, and it was much simpler to take a bit of the
    sand
    | > or
    | > | > eggshell out of the timing glass, to reduce its period. So a whole
    | > range of
    | > | > different time-period glasses came into use. But then, some
    log-lines
    | > were
    | > | > re-knotted, to conform with the new understanding. And just as you
    | > might
    | > | > expect from Sod's law, these were not kept together in associated
    | > pairs, so
    | > | > that over time, some vessels would have a short glass but with long
    | > knots,
    | > | > and others vice versa. It was complete chaos.
    | > | >
    | > | > These problems had afflicted Halley's voyage in 1699-1700 to
    measure
    | > | > magnetic variation in the Atlantic, as described in his journal of
    the
    | > | > Paramore.
    | > | >
    | > | > So much so that in 1763, (around the date of Cook's Atlantic
    voyages)
    | > | > Maskelyne devoted a 6-page appendix of his "British Mariner's
    Guide" to
    | > | > "Some remarks on the proper length of the log-line". Its first
    | > paragraph
    | > | > ended as follows-
    | > | >
    | > | > "...for while one ship has a line of 42 feet between knot and knot
    to a
    | > | > glass of 28 seconds; another, one of 42 feet to a half-minute
    glass;
    | > and
    | > | > another, one of 48 feet to a glass of 28 seconds; all which
    proportions
    | > are
    | > | > very commonly used, their accounts must differ as much from one
    | > another, as
    | > | > most of them do from the truth; for, as only one can be right, all
    the
    | > rest
    | > | > must consequently be wrong.". I relish Maskelyne's pithy prose.
    | > | >
    | > | > George.
    | > | >
    | > | > contact George Huxtable, at  george{at}hux.me.uk
    | > | > or at +44 1865 820222 (from UK, 01865 820222)
    | > | > or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    | > | >
    | > | >
    | > | >
    | > | >
    | > | >
    | > |
    | > |
    | > | --
    | > | Keeping up with the grind
    | > |
    | >
    | >
    | >
    | >
    | >
    |
    |
    | --
    | Keeping up with the grind
    |
    
    
    
    
    

       
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