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    Re: Two reckonings
    From: John Huth
    Date: 2011 Jan 3, 11:54 -0500
    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. 


    John H. 

    On Sun, Jan 2, 2011 at 7:26 PM, George Huxtable <george@hux.me.uk> 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

    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

    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

    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.


    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.

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