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    Re: How Many Chronometers?
    From: Frank Reed
    Date: 2009 May 10, 23:07 -0700

    Greg, in the opening of this thread, you wrote:
    "When a time tick or other master reference is not available then by what 
    means can a navigator at sea use to determine whether a chronometer is 
    maintaining a consistent rate. If two chronometers are carried then an 
    inconsistency between the two would suggest a problem but then which 
    chronometer is at fault? How about a third chronometer to help the navigator 
    determine which chronometer is behaving badly. Carrying three chronometers 
    does triple the chances of one going down but since quartz watches are cheap 
    why not carry three?"
    My interpretation of your question may be a little different from the other 
    replies you received. I read this message to mean that you were asking about 
    the general issue of N chronometers. Here's some thoughts...
    You can't trust it! Some people in the early days of chronometers came very 
    close to arguing just that. But that's surely over-kill. A better policy 
    would be to bear in mind that there is some steadily increasing probability 
    that the chronometer has gone wrong. How much probability? Well, that depends 
    on the chronometer and the user. Modern quartz watches have such high 
    reliability that the probability is negligible on any voyage less than many 
    months away from land or contact with other mariners, and when would that 
    every happen in this century? But 150 years ago, even after a month, you 
    might want to consider a significant probability that the rate has changed.
    Some folks argue logically that two chronometers is no better than one since, 
    if they disagree, you have no way of knowing which one is wrong. That's 
    perfectly true, in theory, but in practice two chronometers back each other 
    up. If they agree, you very likely have nothing to worry about, even if you 
    have no time check for months on end. And if they suddenly disagree, THEN you 
    have good cause to use other means to get a time check. Hail another vessel, 
    or get on the radio and ask, or listen for a radio station with an 
    established reputation for an accurate time tone at the top of the hour 
    (e.g., I can pick up WCBS in New York from hundreds of miles away at night).
    Things get interesting as we go to higher numbers. You can trust the group in 
    the set that agree, right? But the probability of a failure of one 
    chronometer increases with each additional instrument that you carry. So if 
    we have two that agree within a second, and one that is ten seconds 
    different, what should we do? With traditional mechanical chronometers, you 
    might get a sudden fixed jump in rate which would be detectable as a steady 
    drift in the error of that aberrant chronometer as the days pass. We can then 
    toss that one. Or should we assume random-walk errors and just average up all 
    the indicated times? That might be a good policy, but then again, if the 
    chronometer stops dead, you know you wouldn't average in its reading. So 
    there's a limit to the averaging policy, too...
    This is perhaps all "academic" today since quartz watches are so excellent, 
    but I still agree with your comment that 'since they're cheap, why not carry 
    more?' The probability of a change in rate of a single quartz watch may be so 
    very low that it's not worth noticing, but there's still a chance you could 
    drop your sextant on it.
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