NavList:

For longitude without instruments, you could memorize the details to calculate minima of the eclipsing binary star Algol (http://en.wikipedia.org/wiki/Algol). Then you watch the sky every night waiting for it to dim. You carefully observe and plot its magnitude for several hours around the minimum of one of its ten-hour eclipses while simultaneously making observations for local apparent time. The minimum gives you GMT based on the numbers you've memorized (assuming you know the date within one or two calendar days --if you don't, you could get that from the phase of the Moon if a common calendar is permitted by the rules of the game). The data that one would need to memorize for Algol eclipses are as follows:
Base date: May 8, 2012, 04:28 GMT
Period: 2.867362 days (2d 20h 49m 00s)
Light delay: -7.7 minutes on Feb. 7, +7.7 minutes on Aug. 7.
Note that the base date could be updated in advance to make the calculation shorter.

With visual observations, you would not be able to estimate the time to better than about fifteen minutes, but with averaging over a few cycles you might do as well as ten minutes. The calculation of the times of the minima is simple enough in principle. You just add multiples of the period to the base date and time (it's easiest to add 3 days and then subtract 3 hours and 11 minutes. The light delay could be omitted, but it's interesting so I'm throwing it in. The eclipses are seen earlier when the Earth is closer to Algol which occurs around February 7 of every year. So on that date you would subtract 7.7 minutes. Six months later, when the light from Algol has farther to travel to reach the Earth, you add 7.7 minutes. In between it's a sine curve which can be easily estimated to sufficient accuracy by eyeball.

The local time observation can be done by meridian passage of stars assuming you're on land. I think you could get local time this way to within a couple of minutes so GMT from the Algol eclipses is still the limiting factor.

It shouldn't be difficult to get latitude to half a degree by the usual observations. This method for finding longitude would be accurate to 15 minutes of time or a little better so that's roughly 3-4 degrees of longitude. Also note that you have to wait for eclipses, and it could be a long wait. There's the nearly three day period, but also the eclipses often occur in daylight so you may have to wait weeks for the necessary observations. Finally, there are fainter eclipsing binaries with much more sharply defined eclipses (and as regular as Algol), so if you can bring a telescope, you can get longitude more accurately with carefully selected stars. But then you might as well use the eclipses of Jupiter's moons.

Alternate method: you bring along the 1837 edition of Bowditch's "New American Practical Navigator" which includes many excellent methods for finding longitude, and you walk up the first person you see and say, "if you tell me where I am, I will give you this antique book which you can sell on ebay for at least $150." :)

-FER

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