# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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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
the general issue of N chronometers. Here's some thoughts...

N=1:
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.

N=2:
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,
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).

N>=3:
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

-FER

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