http://en.wikipedia.org/wiki/Method_of_lunar_distances
Effect of Lunar Distance Errors on calculated LongitudeA lunar distance changes with time at a rate of roughly half a degree, or 30 arc-minutes, in an hour.[1] Therefore, an error of half an arc-minute will give rise to an error of about 1 minute in Greenwich Time, which (owing to the Earth rotating at 15 degrees per hour) is the same as one quarter degree in longitude (about 15 nmi (28 km) at the equator).
so without a clock its posible to measure longitude with 28 km mistake just with sextant and tables
one year of spheric trig, one of astronomy, one of navigation learning that the only solution of the longitude problem was clocks and thats no more after this thread
edit:
well in any case ill go on with my device to see if somone slips it though history
basically its a solar clock with a disc turning aiming at the moon with a needle you dealy each day 1/28
from greenwhich the needle on the disc aiming at the moon will always coincide with the sun shadow
now if youve traveled 180º east both needles ( the moon needle and the sun shadow) will have offset 24 hours
so 90º 12 hours
45º 6 hours
22º 3 hours
11 1.5 hours
5º 45 minutes
2º 22 minutes
1º 11 minutes
the days which you can see sun and moon you could measure very precisely