[stan_rogers]

Sunrise and sunset together will give you local noon (or local midnight). Local noon plus an accurate timepiece set to a known location will give you a time offset. Knowing your time offset is equivalent to knowing your longitude (which was the whole purpose behind the Harrison chronographs). You won't know it to a tremendous accuracy, since you can't get the exact moment of sunrise or sunset, just a vague idea, your position is likely to change between sunrise and sunset, and dead reckoning on a featureless sea under a featureless sky can only be so accurate. But it's knowing the difference between local time and a reference time that gets you longitude.