I'm reading the Island of the Day Before, by Umberto Eco, so of course I've been thinking a bit about longitude.
I'm sort of confirming this, but if you wanted to find your longitude (compared to say, Greenwich), and didn't have a good clock, one way to do it would be to find your latitude, and then use a universal measure of time (i.e., an event that would be seen at the same time wherever you are on the earth, as long as you can see it). And the one event that is pretty much seen at the same time (sinceI think there is relatively little parallax) is the transit of Jupiter's moons.
So I guess that you would need three things. (1) a small telescope, (2) a chart to know what time it is at your latitude, say a chart that shows what stars rise at what time at what latitude at what time of year, and (3) a chart showing what time Jupiter's moons transit.
Is this pretty much correct? Maybe there's an easier way to tell local time. And also, I think that there wouldn't be much parallax with Jupiter, because again, I'm not positive.