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    Re: Upside-down sextant test.
    From: Steven Wepster
    Date: 2001 May 01, 8:22 AM

    Dear George,
    Last weekend I did the sextant test that you described on april 21st. I have now
    two sextants at my disposal:
    A. Freiberger drum sextant, reading to 1', 4x magnification;
    B. Heath & Co with tangent screw and vernier (1944), reading to 0'2, magn. 3x.
    The target was the steel structure of a disused railway bridge, about 1km away.
    I did the measurements through window glass and I did not step on the Bowditch
    (or anything else) to compensate for the spin axis/telescope distance. In fact, I
    didn't have your request around, only a vague remembrance of it.
    For both sextants I made 4 sets of 10 measurements. The sets were:
    1. sextant upright,  increasing the angle
    2. sextant upright,  decreasing the angle
    3. sextant reversed, increasing the angle
    4. sextant reversed, decreasing the angle
    Assuming the measurements follow a normal distribution with unknown mean and
    deviation, one can construct 95% confidence intervals for the mean of the
    distribution, using the mean of the measurements as an estimator. This allows one
    to make statistically justified conclusions.
    The results were as follows.
    A. Freiberger
    set   mean   deviation  95% confidence interval for mean
     1    0'.04   0.21       -0.11 ... 0.19
     2   -0'.06   0.20       -0.20 ... 0.08
     3    0'.40   0.38        0.13 ... 0.67
     4    0'.46   0.31        0.24 ... 0.68
    B. Heath
    set   mean   deviation
     1    0'.42   0.31        0.20 ... 0.64
     2    1'.14   0.31        0.92 ... 1.36
     3    0'.77   0.34        0.53 ... 1.01
     4    1'.60   0.25        1.42 ... 1.78
    For the Freiberger sextant, there is an increase in measured angle of about 0'.4
    when holding the sextant upside down. The same holds for the Heath. In addition,
    the Heath shows an even greater sensitivity in the direction of approach,
    increasing or decreasing the angle. I suppose this is due to wear and high age.
    The effect is not statistically significant for the Freiberger sextant.
    I think it is remarkable that in both cases the measured angle increases when the
    sextant is held upside down. That discounts movement of the alhidade relative to
    the frame as the main cause of the difference. Such a movement, when induced by
    gravity, will increase the distance between the mirrors and consequently decrease
    the measured angle.
    Regards, _Steven.
    ---- original message ----
    I wonder if any of you owners of expensive metal sextants would like to
    participate in a simple little experiment.
    Look at the horizon through your sextant, preferably from a stable
    platform, using as much magnification as you can. If you're on land, a
    rooftop or hilltop or some other convenient horizontal target will do just
    as well. It doesn't matter whether it's distant or local. Nor does it
    matter whether the target is in a horizontal direction from you, but it
    shouldn't be higher than a few degrees. Avoid viewing through window-glass.
    Now adjust the screw until the two images of the target or horizon are
    aligned, just as you would when checking the index error. Now record the
    sextant reading, as precisely as you can. It will be somewhere close to
    zero degrees. For nearby objects, it will normally be a negative reading
    (i.e. off the arc).
    Next, standing at the same spot, invert the sextant, and make the same
    measurement again. Make sure that the final adjustment is made with the
    screw moving in the same direction each time (for me, always clockwise).
    For ultimate accuracy (though it won't make a lot of difference), for the
    inverted measurement, stand on a book of height h, where h is the vertical
    offset of your sextant from the telescope line to the pivot point. Volume 1
    of the 1977 Bowditch is just thick enough to match my sextant perfectly!
    This will put the two sightlines of the inverted sextant into exactly the
    same place as they were before, but interchanged.
    In theory, the two readings should be exactly the same. But a sextant will
    flex slightly, on account of the gravity stresses due to its own weight,
    which reverse with respect to the sextant body when it is inverted. In
    particular, a slight flexure of the mirror mountings may occur, or perhaps
    the whole frame or the index arm may flex slightly. It's not obvious, to
    me, which way the readings would be expected to change, and by how much.
    But the more rigid the sextant, the less the change should be, and such a
    test may be a useful way to evaluate this aspect of an instrument and
    testing for any looseness before taking it out of a shop.
    All I have to go on here is my cheap Ebbco plastic sextant. A plastic frame
    is of course much less rigid than a metal one, but on the other hand the
    weights involved are considerably less. When I check this against a nearby
    roof ridge, I find that because of the simple nature of the Ebbco (and the
    limited resolution of the ageing human eye) there's a scatter in each
    observation of plus-or-minus 1 minute or so. It's then necessary to average
    10 observations. In the normal orientation I get a mean-of-ten reading of -
    23.2 minutes. That is, 23.2 minutes away from xero, off the arc. With the
    sextant inverted, the average is -24.6, 1.4 minutes more negative. Not a
    big change, but a measurable one.
    If any list member with a more exotic sextant is prepared to make a similar
    measurement, I would be most interested to learn the result, and whether
    the difference is large enough to be measurable..
    Why am I interested in the upside-down behaviour of a sextant? Well, it's
    connected with an instrument for measuring the observed dip of the horizon
    at sea, the Blish prism. And inversion of the whole sextant-prism
    combination seems likely to provide a simple way of finding any zero error
    in the instrument, so that an absolute value of dip can be obtained. Any
    flexure of the sextant, on being inverted, would complicate this process
    and need to be corrected.
    More about the Blish prism will follow shortly.
    George Huxtable
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.

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