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    Re: How Many Chronometers?
    From: Gary LaPook
    Date: 2009 Sep 15, 02:22 -0700

    Based on our discussion, I became curious about the accuracy of digital
    watches and their suitability for use as chronometers so I went to my
    local TARGET store and purchased three identical watches for $17.00
    each, the cheapest that they had. I set them and let them run for a few
    days and, as I expected, they each had different rates. Based on this I
    labeled them "A", "B", and "C" in the order of their rates starting with
    the slowest. I then reset them to UTC at 0121 Z on May 28, 2009. I
    checked them against UTC from WWV eleven days later on June 8th and
    found that they were all running fast by 2, 4 and 7 seconds respectively
    and I worked out their daily rates as .1818, .3636, and .6363 seconds
    per day, respectively.
    On July 11th, 44 days after starting the test, the watches were fast by
    9, 17 and 28 seconds. Using the rates determined in the first 11 days
    the predicted errors would have been 8, 16 and 28 amounting to errors in
    prediction of 1, 1, and 0 seconds. If using these three watches for a
    chronometer we could average the three errors and end up with only a .66
    second error in the UTC determined by applying the daily rates to the
    three displayed times after 33 days from the last check against WWV
    which took place on June 8th.
    I determined new rates now based on the longer 44 day period of .2045,
    .3864 and .6363 seconds per day, respectively.
    On September 15th at 0800 Z (per WWV), 110 days after starting the
    test,  I took a photo of the watches which I have attached. The photo
    shows the watches fast by 21, 41 and 69 seconds but by carefully
    comparing them individually with the ticks from WWV the estimated actual
    errors are 21.5, 41.8 and 69.0 seconds. Using the 44 day rates, the
    predicted errors are 22.5, 42.5, and 70 seconds giving the errors in the
    predictions of 1.0, 0.7 and 1.0 seconds which, if averaged, would have
    caused a 0.9 second error in the computed UTC after 66 days from the
    last check against WWV on July 11th.
    If, instead, I used the 11 day rates then the predicted errors would
    have been 20.0, 40.0, and 70.0 seconds which would result in errors of
    prediction of -1.5, -1.8, and 1.0 which, if averaged, would cause and
    error in the computed UTC of -0.6 seconds after 99 days from the last
    check against WWV which would have been on June 8th in this example.
     From this experiment it appears that fifty one dollars worth of cheap
    watches would give you a perfectly adequate chronometer.
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