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    Re: Intended High Resolution Chronometer
    From: Frank Reed
    Date: 2014 Feb 26, 11:04 -0800

    Thanks for the photo, Brad. Here's a little fun with it...

    Using late 18th century technology, a clock with a one-week "day" hand, just like the one in your photo (ever so slightly modified!), would be readable to a precision of +/- TWO SECONDS of time --without adding any extra hands to the clock. Surprising, huh? Here's how I got there:

    That "day" arm on that clock moves through 51.4° in one day. And we know that the Moon moves across the sky about 13° per day (four times more slowly since the Moon takes four weeks to orbit the Earth), and yet late 18th century navigators could measure that motion to an accuracy on the order of +/-15 seconds of time, equivalent. I'm assuming a really good sextant and all other conditions excellent. A factor of four faster motion for the "day" arm compared to the Moon would yield +/-4 seconds of time. But the sextant's double-reflection cuts the Moon's motion in half: each day it moves only 6.5° as an angle measured on the arc of the sextant (just another way of saying that the sextant's arc angle of 60° actually contains 120° of divisions on the arc). That's another factor of two. Therefore we could read this clock to +/2 seconds. You can also go the direct route and ask how +/-5 arcseconds on the arc compares to 51°, and you'll get the same result (again, divided to a precision of 10 seconds is equivalent to 5 seconds on the actual arc). Of course to make that happen in practice, you would need to divide the dial around the rim of the clock as finely as the scale on a high-end 18th century sextant. A dial made of platinum might push the price of the clock up a bit. You would also need to attach a vernier to the end of the "day" hand. A magnifying glass would be a necessity! But there would no other moving parts.

    Of course reading a vernier is a real nuisance, so it would be easier to add some rotating scales or hands that are geared to the main motion of the clock. In other words: add hour, minute, and second hands, as expected on a normal, functioning clock designed to read to seconds. Turning back to sextants and their ability to read fine angles, that, after all, is ALSO exactly what happened to sextants in the early twentieth century! A micrometer is a "minute hand" geared to the main motion of the index arm. It took over a hundred years for that simple concept to be applied to the sextant itself.


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