NavList:

Brian Villmoare, you wrote:
"I had set up a problem where you have a fixed-angle sextant, because I am trying to figure out if it is possible to get latitide from the Sun with a Bris sextant. But, you also have a timepiece, and can take the angle as the Sun goes up, then down. So, mathematically (if not practically), longitude is straightforward (given the Equation of Time) with the Bris sextant. "

There are two approaches to this problem. First and foremost, it's just two altitudes with known UT/GMT. So you generate lines of position from each by whatever method you like, advance the earlier one based on vessel motion and cross them. And there you have your latitude and longitude.

The other approach is to hop in your time machine and travel back 200 or 250 years. Back then you could record time intervals with a common watch. So you could measure the altitude of the Sun in the morning. Then measure again a few hours later. And reliably, with reasonable accuracy you could record the elapsed time to the nearest few seconds. With the pair of altitudes and the elasped time, you could determine the latitude. This was a popular historical problem which excited land-based mathematicians, but it was really too much trouble for most navigators in practice. I'm attaching an example from the first page of an article in the Transactions of the Royal Society from 1799. You can read the rest here if you want to get into the historical methodology, but remember: this is just one of many explorations of this idea, and it's strictly historical. For other historical problems and approaches, you may want to look at the NavList historical book index. For a modern navigational context, it's just two lines of position crossed for a running fix.

Frank Reed

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