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    Re: How Many Chronometers?
    From: Gary LaPook
    Date: 2009 Sep 15, 10:24 -0700

    It wouldn't seem that motion would affect their rates.
    They have spent the last 110 days next to each other in a cabinet
    where the temperature is pretty constant. According to the recording
    thermometer in the room, the temperature stayed in the range of 66� to
    82� F. But since I didn't think ahead,  I didn't reset the memories in
    the thermometer when I started the experiment so the recorded
    temperature range actually covers a longer period of time than the 110
    days so the temperature swings experienced by the watches might have
    been somewhat less but I have no way of knowing.
    To deal with the temperature issue, place the three watches in a small
    box with some kind of insulation (or wrapped in a blanket) to smooth
    out temperature swings and keep it below decks which is where
    chronometers were traditional kept.
    On Sep 15, 9:09�am, Lu Abel  wrote:
    > Gary:
    > A fascinating experiment and experimental confirmation of my long-held
    > belief that even the cheapest digital watch makes a superb chronometer.
    > Now a challenge for anyone wanting to repeat the experiment or extend
    > the results:
    > 1. � Take the "watch board" and simulate motion. � Okay, maybe we can't
    > take it to sea but maybe drive it around town with us?
    > 2. � Vary the temperature. � Maybe put the board outside in direct
    > sunlight (and rain and maybe even snow).
    > Remember, Harrison's biggest challenge was not making an accurate
    > chronometer (that had been done already) but rather making one that
    > remained accurate despite the motion and temperature changes experienced
    > at sea.
    > Whoops, as I write this I'm looking at my digital watch on my wrist and
    > watching it bounce around. � Maybe experiment #1 isn't required. � In
    > fact, the very nature of digital watches should make them
    > motion-insensitive (excluding relativistic effects :-P ).
    > Lu Abel
    > Gary LaPook wrote:
    > > 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.
    > > gl
    > > ------------------------------------------------------------------------
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