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    Re: Sextant calibration.
    From: George Huxtable
    Date: 2007 Apr 21, 10:05 +0100

    Following my confession of a weakness for examining everything I come
    across, for the purpose of picking out error, Alex tells us that he operates
    in just the same way. He and I are planning to meet up, in Oxfordshire,
    later this year. Which may make for a successful meeting of like minds: or
    will it end up with mutual annihilation? We can only wait and see.
    
    ============================
    
    Frank introduces us to a work that's new to me, and presumably to most of
    this list.
    
    | By the way, there was, in fact, a very good eighteenth century  method of
    | calibrating sextants. I've seen it written up in the "Tratado de
    Navegacion" by
    | Jose de Mendoza y Rios, who was one of the great experts on the  subject
    in
    | that period, especially after he transplanted to England. The way he
    describes
    | it makes it sound like a relatively well-known procedure.
    
    Mendoza was certainly very knowledgeable about navigation. Based on the
    title that Frank gives, it seems that the work is in Spanish, which
    presumably Frank can handle, though I can't. Is there an English
    translation?
    
    The procedure Frank describes seem to have some similarities with my own
    suggestion, in Navlist 2608, as follows-
    
    "One could readily compare one instrument against
    another, at spot values, by comparing horizontal-angle spacings between
    known distant landmarks, such as tree-trunks."
    
    But that was only for intercomparison of one instrument against another.
    Frank seems to be saying that it can be adapted for absolute measurement of
    angle, by using the fact that angles summed around the horizon must add up
    to exactly 360 degrees. I can see how that is used as a check, by surveyors,
    of the truth of a round of azimuths, but haven't yet understood, from
    Frank's explanation, how it could be used to pin down where, in what part of
    the arc, such errors occurred.
    
    Frank wrote-
    "Suppose, for example, I have steeples within a  few degrees of
    | the cardinal points of the compass. Call them N, E, S, and W.  Suppose I
    measure
    | the angle NE and find that it's 90d 10'. Then I measure angle  ES, SW, and
    WN
    | and find that they are 89d 05', 91d 12', and 89d  31'. From these
    | measurements, I can deduce that there is an arc error at 90  degrees
    of -0.5' of arc
    | --because the measured angles don't add up to 360  degrees."
    
    For the life of me, I can't see how that deduction follows. Why couldn't
    that error of -0,5' of arc be elsewhere than at 90 degrees? Am I missing
    something obvious here? How did Mendoza explain it?
    
    The puzzle is that Frank states later-
    
    "This calibration method also works on the Connecticut coast at various
    places since you can find lighthouses and other fixed markers. I've tried
    it."
    
    Also, I accept that using some sort of theodolite, rotated round a pivot
    which had been set vertical using a spirit level, the total of all azimuths
    must add to 360.  But I don't see how that could apply to the horizontal
    angles of land-objects with a hand-held sextant, unless they were all
    constrained to lie in a horizontal plane by being at the water's edge (such
    as on the Connecticut coast). In a city, church steeples will be far from
    coplanar, wherever they are measured from.
    
    And that takes me to a final semantic quibble. Frank wrote-
    
    "You climb to the top of any suitable
    | tower or steeple and then you shoot horizontal angles between well-defined
    marks
    | on steeples in the distance around you"
    
    Well, climbing to the top of a tower, with sextant in hand, and a table to
    place it on, might be feasible, but trying the same thing from the top of a
    steeple would be decidly uncomfortable, if not impossible.
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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