Thank you. Lunar distance might work.
I was too brief in OP. I do not want to use something who's validity can not be checked on the spot. Or maybe made on the spot. Compasses can be.
I will take a flight across the pacific and I want to know how far the new time zone is from the one I left. I will watch sand-glass clocks and repeatedly listen to an audiobook's single chapter to calculate the time difference. Then check if the sun is in the right place.
You did read the requirements, I hope?
"The only tools required are a
good quality metal sextant (the plastic ones are not adequate for lunars),
the Nautical Almanac, and an inexpensive scientific calculator."
To "calculate the time difference" your watch or phone timer is far more accurate than any "sand-glass clocks".
You really can't achieve anything with what you are planning.
Finding longitude, even with an extremely accurate clock needs very precise measurements.
Here is a comment from someone who knows
An expert navigator, with a steady hand & accurate sextant and timepiece, can determine their position to within half a mile. These accuracies are usually achieved on shore.
If you're bobbing around on a small boat, an expert would be very happy to get to within a mile or two of the correct position. In fact, most of us would be satisfied with the previously mentioned 4 - 5 nm accuracy.
Since sextant angles are measured in degrees and minutes of arc (1/60th of a degree), measuring this angle to an accuracy of 1 minute of arc (1') will result in a positional accuracy of 1 nautical mile.
Accurate sextants can measure this angle to an accuracy of 0.2'. This suggests that, theoretically, one could determine their position to 1/5 of a mile.
Additionally, a good clock is required to accurately compute the GP of the celestial body. An error of 1 second in the clock will create a positional error of up to 1/4 of a mile.
From Cruiser''s Forum, Acceptable Accuracy in Celestial Navigation[/b]]=http://www.cruisersforum.com/forums/f121/acceptable-accuracy-in-celestial-navigation-53980.html
Cruiser''s Forum, Acceptable Accuracy in Celestial Navigation