NavList:

Greg, you wrote:
"The time sight at prime vertical is the ideal observation for recovering time if the chronometer should ever stop."

It was historically, and in the days of the "Old Navigation" a substantial fraction of navigators apparently knew and understood this. But with traditional chronometers there was the risk that a stopped chronometer would dramatically alter its rate. And the rate is everything. Setting the chronometer to the right time is a helpful convenience, but what you really want to know is how much the difference between the displayed time and GMT changes from day to day. Of course, we can recover the rate by repeating the time sight over a series of days, the more the merrier.

Now turn to the "New Navigation". Everything is a line of position, including Noon Sun and time sights, too. So suppose your chronometer has stopped, but you have a good estimate of the correct time, maybe from a common wristwatch that was set from the chronometer a few days earlier (or from a lunar if you don't even have that). Treat its time as correct, and plot as many LOPs as you can using your favorite methods. You reduce the error in the resulting fix by shooting dozens of sights, assuming you're in port. Next you apply the usual procedures to estimate an error ellipse around that fix. In general, the error ellipse is reduced in size in proportion to the square root of the number of sights --the fix from 16 sights is only twice as accurate as the fix from 4 sights, all other things being equal. When the error ellipse is small enough to satisfy your standards, you compare the longitude of the fix with the known longitude of the port. The difference in longitude, of course, converts to difference in GMT at the rate of four seconds per minute of arc of longitude.

Now we can go back to the "Old Navigation" method and refine it based on the modern science of LOPs. The only real difference is that we shoot lots and lots of sights and average the results, and we know the square root rule. Since we're assuming we're at a known location, the latitude is never in question so we can shoot time sights all day long avoiding only those that are really close to the meridian, let's say within 20 degrees.

Then there are lunar time sights. Instead of shooting an "actual" lunar distance where we measure the angle between the Moon and the Sun or a star, we can measure the altitude of the Moon and use it for a time sight. The resulting local time should match the local time from a Sun time sight. If it doesn't, you change the assumed GMT until they match. This is, of course, equivalent to plotting a standard LOP for a Moon altitude along with other LOPs (a method independently discovered by a number of 20th century navigators including Letcher and Chichester). If the Moon LOP passes through the fix from the other LOPs, then your GMT is correct. If it passes east or west, then your GMT is wrong, and you adjust it until they match. In order to get a meaningful measure of GMT by this technique, the Moon should be more or less "sideways" in the sky with the horns of the crescent (or the poles at other phases) more or less parallel to the horizon. Though this all works, it's relatively low accuracy.

Just some thoughts...

-FER

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