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    Sextant calibration in the workshop
    From: Bill Morris
    Date: 2007 Dec 24, 14:30 -0800

    It may be of passing interest to members to learn how a sextant may be
    calibrated in practice in the workshop, though not with equipment
    readily available to the amateur. Two autocollimators and a surface
    plate are needed. A rotary table is an extra refinement and is not
    strictly necessary. The rotary table is not used as part of  the
    calibration process, but to rotate the sextant to the desired position
    easily
    
    A collimator is simply a lens with an illuminated graticule at its
    focus, so that a parallel beam is projected and the image of the
    graticule appears as if at infinity. If the beam is intercepted by a
    mirror that is normal(square to) the optical axis of the collimator,
    it gets reflected right back to where it came from. If the mirror is
    at some angle to the optical axis, the reflected image is displaced.
    In the autocollimator there is an optical arrangement called an
    optical micrometer that allows the reflected image to be viewed and
    its displacement to be  measured directly. The amount of displacement
    is dependent only on the focal length of the collimating lens and the
    angular displacement of the mirror, not on the distance of the mirror
    from the instrument.
    
    Unlike length measurements, angular measurements require no official
    standard to be kept, as there are always exactly 360 degrees in a
    circle and 180 degrees in a straight line. This latter fact is
    exploited in the calibration method. The two autocollimators are first
    set up on a surface plate, a polished slab of granite about 1000 x 600
    x 100 mm and flatter to better than 4 microns, so that their vertical
    cross-wires coincide with each other. One is designated as the "fixed
    autocollimator" and the other the "moving autocollimator" The sextant
    is adjusted on a suitable stand so that the plane of its arc is
    parallel to the surface plate and is set carefully to, say, 15 degrees
    or some other factor of 180. Its index mirror is then placed in the
    light path of the moving a/c and the whole sextant rotated until the
    reflected image is seen in the a/c to coincide with the vertical cross
    wire. The sextant is then set to 0 degrees, taking great care not to
    move it on the surface plate, and the moving a/c moved until the
    reflected image again coincides with the vertical wire. The sextant is
    reset to 15 degrees and so on.  After repeating this 24 times, the
    sextant will have rotated through a nominal 180 degrees and the axis
    of the fixed autocollimator will then be normal to the index mirror of
    the sextant. Any excess or deficit can be measured by the fixed a/c.
    
    The excess or deficit represents 24 times the error of the sextant in
    moving through 0 to 15 degrees; and the axes of the autocollimators in
    their final positions will be at a known angle of  7 1/2 degrees plus
    or minus this error(The index mirror rotates through 7 1/2 degrees,
    though the sextant index reading moves from 0 to 15). This known angle
    can then be used to calibrate the rest of the scale, from 15 to 30, 30
    to 45 degrees and so on. Alternatively, if many sextants are to be
    calibrated, one of the a/c s can be adjusted to remove the error and
    bring the axes to exactly 7 1/2 degrees, allowing the sextant error of
    any step to be read off directly from one of the a/c scales. Needless
    to say, once the a/c s reach their final positions they must not be
    disturbed.
    
    Errors for values greater than 15 degrees that are factors of 180 can
    also be estimated ie. 120 degrees(3 steps, see attachment), 90
    degrees(4 steps) 60 degrees(6 steps) and 30 degrees(12 steps). I am
    not brainy enough to be able to state with certainty what effect the
    number of steps has on the probable error of the result. Perhaps Alex
    Eremenko can help?
    
    Members may wonder about the precision of an autocollimator. A basic
    Hilger and Watt Microptic autocollimator's least graduation is 0.2
    seconds and with a little practice and a mirror of good quality,
    readings can be repeated to within about 0.3 seconds. Even at first
    acquaintance, repeatability to within 1 second is easy. Using a
    photoelectrical readout, precision is about five times better. Its
    accuracy is of a similar order. When measuring to parts of a second,
    great care is needed. The instruments need to be given time to reach
    the ambient temperature, overnight if possible, touching them should
    be kept to a minimum and accidentally brushing against an
    autocollimator when stepping out the 7.5 degree increments can mean
    having to go back to the first of 48 readings again.
    
    The setting error of the sextant is greater. Its micrometer is
    altogether coarser than those of the autocollimators, its thimble is
    much smaller, making for larger reading errors, the oil film
    separating the parts will vary in thickness depending on temperature
    and speed of setting, the whole instrument is liable to move when
    resetting it unless very great care is cultivated and taken and the
    error also contains the autocollimator reading errors. I may have left
    something out! Even so, in a series of 24 repeat readings with a SNO-T
    sextant, 95 percent of readings can be expected to fall within a range
    of 3.7 seconds.
    
    In setting the sextant micrometer, it must always be rotated in the
    same direction to avoid backlash errors. In sextants like the SNO-T
    and Freiberger, it does not matter in which direction, as long as it
    is always the same, but in the BuShips Mark II and sextants of similar
    construction including Tamaya and clones, there is only one correct
    setting direction.  As it has only one thrust bearing, preloaded by a
    rather weak spring, it must be rotated so as to load the thrust
    bearing, not the spring. In the MkII, this happens to be the direction
    that decreases the reading of the instrument.
    
    The micrometer can be calibrated directly against one of the
    autocollimators  and here the superiority of the SNO-T over the Mk II
    shows itself. The maximum deviation of the SNO-T from 0 to 60 minutes
    in 5 minute steps was 1.6 seconds, compared to 6.5 seconds for the Mk
    II.
    
    I am now in a position to answer George Huxtable's question "Has
    anyone on this list, by measuring star-star distances or by any other
    method, ever discovered reproducible errors, outside the terms of a
    calibration certificate or maker's warranty, in a sextant? Has anyone
    made calibration measurements of his own, in which he has more
    confidence than in the manufacturer's scale readings, corrected as
    necessary by the box certificate? And if the answer is yes, what's the
    magnitude of those errors?"
    
    According my SNO-T manual in English translation K52.514.004 TO of
    1976, "Instrumental accuracy within angle range 0 to 120 degrees - +/-
    6 seconds" and "Accuracy of drum scale reading - +/- 6 seconds". Alex
    Eremenko's Russian manual gives "Instrumental error within the range
    of measurement - 12 seconds" I have already dealt with the micrometer.
    My 1981 instrument meets Alex's specification but not mine:
    15d. +1"; 30d +1"; 45d +4"; 60d +7"; 75d +8"; 90d +11"; 105d +9"; 120d
    +8".
    
    My Mk II s/n 14176, 1942 in near-new condition with a certificate from
    Long Beach Shipyard dated 7 January 1986, does well too, except above
    90 degrees. I give the original certificate figures followed in
    brackets by my own, which are each based on the mean of three careful
    readings: 15d +3"(+1"); 30d -14"(-12"); 45d -17"(-16'); 60d
    -25"(-22"); 75d -30"(-31"); 90d -33"(-40"); 105d -12"(-31"); 120d
    0"(-30"). For most practical purposes except lunars, the differences
    are insignificant.
    
     If someone can tell me how to add attachments to the list I will post
    a diagram and a photograph to make the process plainer.
    
    Bill Morris
    
    
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