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    Re: Wires, back sights and collimation
    From: George Huxtable
    Date: 2004 Nov 26, 00:30 +0000

    Alex wrote-
    >2. Inspecting the formula, we see that there is indeed a big
    >problem with measuring distances close to 180 degrees,
    >when the tan(A/2) blows up.
    >This is the mathematical explanation of why
    >a) the quadrant with back sight feature cannot be
    >used as a dipmeter, and
    >b) why everyone experienced the problems with finding
    >the index correction for back sights with Wollaston method.
    >(See my previous messages on this subject. I can conclude
    >from his paper that Wollaston did not actually experiment
    >with a quadrant, just speculating on the basis of
    >"thought experiments":-)
    >Same difficulties should occur with "periscope method"
    >by Blith as described by George, and with George's
    >self-made periscope attachment.
    Later, he followed it up with-
    >The formula I gave in my previous message is correct
    >but my interpretation of it is totally WRONG:
    >On Wed, 24 Nov 2004, Alexandre Eremenko wrote:
    >> The source of error is that you cannot determine precisely
    >> the point on the horizon which is exactly "below" the body.
    >and also wrote:
    >> When h is close to 90 deg, this error becomes large.
    >This is not so. Sorry.
    >I am looking for a correct explanation.
    Thanks to Alax for being man-enough to point out his own errors. But I am
    not sure how much Alex is retracting here.
    Is he retracting his paragraph 2, which shows "a big problem with measuring
    distances close to 180 degrees"? If so, then the rest of this note is
    irrelevant. If not, then it may be worthwhile my pointing out that his "big
    problem" does not accord with my own experience with such a device.
    In the case of measuring the angle between fore and aft horizons in
    opposite directions, using a Blish (not Blith) periscope, the angle between
    them will be very near 180 degrees: in fact, it will only differ from 180
    degrees by 2 x dip.
    In which case the factor representing the tan of half that angle would
    amount to about 900: and Chauvenet's formula, if it applied, would indeed
    cause an immense blow-up of any collimation error!
    And I could hardly fail to observe such an immense effect (if it existed)
    as I moved the image of the two horizons across the field of the telescope
    of my modified sextant, or moved my eye with respect to the eyepiece (not
    that I have deliberately made any tests to check for such an effect).
    But I haven't noticed any such effect, so I suspect something must be wrong
    with Alex's analysis. Perhaps Chauvenet's formula is intended to apply only
    to a simple sextant, and  not to the situation where a prism, or an extra
    pair of mirrors, reverses the direction of the light.
    I've dug out my old copy of Chauvenet, but will wait for Alex's response
    before examining the matter in detail.
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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