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    Re: measuring sextant instrument error
    From: George Huxtable
    Date: 2000 Sep 17, 5:31 AM

    Bill Murdoch wrote, about his plan for calibrating a homemade octant-
    >I think I can do it in my garage like this:  (1) Fix a block of wood on the
    >floor with a 1/4" hole drilled in the wood.  (2) Strike an arc just over 100
    >degrees in length with a radius of 6,875.5 mm centered on the hole.  (3)
    >Stand a steel tape measure on edge along the arc so that each 1 minute of arc
    >is 2 mm on the tape.  Replace the pivot bolt in the octant with a longer bolt
    >and place the octant over the block of wood so that the bolt slips into the
    >hole.  That places the index mirror over the center of the circle.  (4) Read
    >the steel tape scale in the horizon glass for reference.  That reading
    >becomes the horizon.  (5) With the index arm set to 0 degrees read the steel
    >tape scale at the spot that is superimposed over the horizon reading.  That
    >begins the calibration.  (6) Move the index arm and note the scale reading
    >viewed in the index mirror that is now superimposed over the horizon reading.
    > If the scale can be read to a half millimeter, the sextant error can be
    >measured to 0.25 minutes of arc.  That is four times better than my usual
    >shooting accuracy and I think good enough for checking a homemade instrument.
    >Think that would that work ?
    >Bill Murdoch
    I think Bill is making heavy weather of all this. A manufacturer (or the
    Navy) would need such a setup where many instruments could be calibrated at
    any time under controlled conditions. Unless Bill is setting up to
    manufacture his octants in quantity, he needs no such thing. He simply
    wishes to make a one-off calibration.
    Nature has provided a well-illuminated object at infinity, known as The
    Sun, and a well-defined plane near the horizontal, known as The Horizon.
    Furthermore, Nature has kindly arranged that over the course of a morning,
    the angle between this Sun and this Horizon sweeps over a wide range of
    values from zero to a maximum at the meridian.
    Astronomers have gone to some trouble to predict the precise motions of
    this body, and almanacs are readily available with the result of their
    predictions. Small corrections need to be made to the predictions, and
    these are well-known and readily applied. Bill has written a calculator
    program which computes all this stuff. The only remaining uncertainty
    relates to abnormal refraction in the atmosphere possibly affecting the
    altitude of the Sun and (particularly) the Horizon.
    A company named Freiberger has taken pains to manufacture an accurate
    sextant, which has already been accurately calibrated, and this is an
    instrument that Bill Murdoch happens to possess.
    What's more, the US military have provided a system, free to any user,
    which allows him to detrmine his precise position on the surface of the
    No doubt Bill possesses a simple Quartz watch which he can set to
    correspond with Greenwich time signals, which are broadcast by radio.
    All these resources are available to Bill. All he needs to do is to take a
    trip to the seaside (or a large lake) on a sunny day, and spend a morning
    by the shore, or on a jetty, with his octant and his sextant. And a
    sunshade. And some way to check his height above water level.
    He needs to find a spot which has a clear view of the horizon, from
    somewhere near East through to South, and to be there by Sunrise.
    There he can spend his whole morning recording times and octant altitudes
    of the Sun, as close together in time as he wishes. He should frequently
    record (but not adjust) any changes in the zero-error, by observing the
    apparent altitude of the horizon. He can interpose (perhaps even alternate)
    Sun altitudes from his precise sextant, to check whether refraction
    conditions in the atmosphere are changing noticeably. He should bear in
    mind that at low altitudes the predictions become unreliable due to to the
    variable effects of refraction.
    When Bill gets home again, he can plot out any deviations between the
    (corrected) altitude predictions from the almanac, and the observations
    from his sextant and octant. This would result in a table of deviations,
    similar to what one uses with a magnetic compass, but hopefully much
    smaller in amount.
    If a convenient viewpoint sees the sea to the West and South, instead of
    East and South, then the job would be done in the afternoon rather than the
    Of course this procedure will calibrate the octant only up to the meridian
    altitude that the Sun reaches at that spot and date. I don't know where
    Bill Murdoch lives, but if it's at a high latitude, he could take his
    holidays at an appropriate spot and date within the Tropics and calibrate
    his sextant there.
    More easily, he can, at home, take angles between the Sun and its
    reflection in a tin tray containing some treacly liquid, such as old black
    engine-oil. The reflection doubles the angular divergence, so for a Sun
    altitude of 45 degrees, the apparent "altitude" between these directions is
    then 90 degrees. This method could be used for the whole operation, intead
    of going to the seaside, and has some advantages, in that the horizon (with
    its problems of uncertainty of dip) doesn't come into the question.
    However, the method presents some difficulies at low altitudes.
    Otherwise, he could arrange to be back at the seaside at dawn or dusk, and
    arrange beforehand to identify a few stars which will then be visible over
    his sea-horizon. They should then have altitudes that allow the as-yet
    uncalibrated gap in the octant's scale (between the Sun meridian altitude
    and the vertical) to be filled in at a number of spot values. The
    measurements could be continued over as long a time as the visibilities of
    the star and the horizon allow.
    I think that Bill Murdoch would be able to achieve an accurate calibration
    of his octant by these methods in less time than it would take him to clear
    his garage enough to provide space for the method he proposes.
    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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