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    Re: Star-star distances for arc error
    From: Bill Morris
    Date: 2009 Jun 26, 00:53 -0700

    Frank and Douglas
    
    ""Also, the measurement can only be done to an accuracy of the divisions of the 
    sextant which in most cases is one minute of arc."
    
    Most modern sextants can be read to a TENTH of a minute of arc. Even sextants 
    which lack verniers on the micrometer can be read to at worst 0.2'. Of 
    course, this assumes that the instrument has been properly adjusted (mirrors 
    perpendicular to frame, telescope axis parallel to frame, etc.) and has no 
    pathological problems, like a loose micrometer, for example.
     
    and you wrote:
    "the certificate indicates accuracy of max error of 1 minute 30 seconds at points on the scale."
    
    But that is a correctable error."
    
    Textbooks of metrology usually advise against interpolation, saying that a 
    value closest to the least graduation interval should be read, so in that 
    respect, Douglas has some support. However, I guess that is advice that is 
    often ignored, probably safely most of the time even when interpolating 
    tenths would take one close to the absolute limits of the instrument's 
    accuracy.
    
    It is worth bearing in mind that calibration certificates for micrometer 
    sextants give the errors only for whole numbers of degrees, every fifteen 
    degrees for NPL certificates, and every twenty degrees for Heath and Co 
    certificates. In doing so, they are in effect calibrating only the rack and 
    centring error. It isn't really all that safe to interpolate, as the sources 
    of error are complex and the errors do not usually vary predicatably over the 
    measurement range of the sextant. Ideally, makers should perhaps also 
    calibrate the worm and its centring errors through a whole rotation. Noone 
    would consider that an engineer's micrometer had been properly calibrated if 
    this had not been done, as well as checking at intervals of, say, 2.5 
    millimetres throughout the measurement range.
    
    The SNO-T sextant handbook claims a maximum error for the drum reading of 6 
    seconds but I haven't come across another sextant that addresses the matter.
    It is a relatively simple and quick matter to calibrate the worm and centring 
    errors of the drum using an autocollimator reading off the index mirror. I 
    have briefly described the instrument in a previous post on calibration in 
    the workshop. Members might be interested in some results.
    
    Yesterday, I calibrated the drums of several common sextants at 5 minute 
    intervals. All are in good adjustment and I took appropriate precautions 
    against backlash. The autocollimator's least graduation is 0.2 seconds. 
    Members may be interested in the results.
    
    The SNO-T met the claims made for it very comfortably with a maximum error of only 3 seconds.
    
    Next best was a Heath Navigation instrument from 1967. It had a maximum error 
    of 17 seconds and most other errors were under 10 seconds, say 3 to 7 
    seconds. 
    
    A well-used Husun sextant from 1938 had errors mostly between 10 and 20 
    seconds, with a maximum of 29 seconds.
    
    A Tamaya 632D sextant from 1957 in apparently excellent condition was no 
    better in one part of the worm with three adjacent readings  giving errors 
    rising from 20 to 31 seconds though most were in the 4 to 10 second range 
    (this surprised me so much that I repeated the readings with similar 
    results).
    
    One might wonder then that some people achieve superb results, and this is 
    probably because averaging evens out the drum and worm errors, which must sum 
    to zero over a whole rotation. I take it for granted that they must also have 
    great observational skills.
    
    Given that they do have the skills, it occurs to me that star-star 
    observations might be at least as good a way of calibrating a sextant as a 
    laboratory method that looks only at whole degrees. One short cut when 
    calibrating an engineer's micrometer is to check it at, say, 2.5, 5.1, 7.7, 
    10.3, 12.9...  and so on, rather than every 2.5 mm as well as a full turn at 
    each end. In effect, this is what star-star distances do in a less structured 
    way.
    
    Bill Morris
    Pukenui
    New Zealand
    
    
    
    
    
    
    
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