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    Re: Star to Star Distances taken on a Second Hand Sextant
    From: Brad Morris
    Date: 2019 Dec 5, 20:59 -0800

    Hi Michael

    Thank you very much for clarifying some of the details of your spreadsheet to me.  It is sometimes difficult to see what someone else had in mind when creating their spreadsheet.  Thank you for taking the time.

    I referred to each of your spreadsheets, to extract the date, time and expected angular distance, with all corrections (refraction, Franks\'s dH, etc) applied.  In the text below, we can see this extraction.  The column labled "datum" represents the value which we will compare your observations to.

    StarStarTimeDateDatum
    ProcyonPollux21154/21/201922.871
    ArcturusAlkaid21105/1/201930.677
    PolluxCapella20354/22/201934.247
    ArcturusAlioth20304/20/201939.875
    AltairEltanin23306/28/201948.652
    ArcturusDubhe20304/20/201953.947

    The first thing you will note is that the datum resolution is to 3 decimal places, or more fluently, 3.6 arc seconds.  That is an order of magnitude more resolution than the observed values, sometimes quoted to  0.5 arc minutes, but usually to a whole arc minute.  The mismatch in precision was somewhat disconcerting to me, as the datum seemed over-resolved given the observation.  We can quibble over this point, but I will not die on this hill :-)

    The other thing I noticed is that Arcturus//Alioth and Arcturus//Dubhe have the identical time and date.  I feel that this is likely a data entry omission error.  I checked two times, certain that it was me.  Alas, I think this bears correction in your data.  Please take a look at your data.

    Why the care and concern about this datum?  I carefully note that most your spreadsheets are treated as a ledger.  This is fine, at some point, user entered data always occurs.  I just want to be sure that the datum presented is correct.  Data entry errors, transposition errors, omissions, and plain old typographical errors are know to slip into the data of the best of us.  The date, time, and your EP are necessary to confirm the datum.  This is a critical and necessary first step.

    Please do take a moment to review the tabular data I summarized above.  

    ========

    Next, permit me to express my relief that the "obs", in cells D68 and E68 represent a series of values, and not just one observation, as was implied by the abbreviation.

    In metrology, we care for two values at the end of the calibration. One is the accuracy of the device, the other the repeatability.  These are derived from a series of observations, not just the one.  My relief at understanding that you had used multiple values was palpable!

    What is now missing from my understanding is the number of observations taken and the actual observed value for each.  It is my hope that you have retained the actual data collected.  This will lead us to the true accuracy and repeatability, three sigma, of your instrument.

    Brad

    In the spirit of disclosure, please understand that I calibrated literally 100's of different, high precison robotic rotary devices for industry, using standard practices (per the NMTBA) and using NIST traceable equipment.  I do understand the process, the procedures and the math.  Of the NIST traceable equipment, the autocollimator and ultradex remain in my hands. These devices permit me to measure rotary performance to with 0.5" for the Autocollimator and 0.5" for the Ultradex, a combined measurement max error of 1 arc second.  Although a topic for another day, with tooling these pieces of kit would allow me to directly calibrate sextants!  In the case of star-to-star distances, the NIST traceable equipment is un-necessary, saving the practitioner of star-to-star calibration 10's of thousands of dollars.  This makes calibration accessible to all

       
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