Longitude with no Chronometer

Measuring the latitude of your current location is fairly straightforward. Just subtract the sun's elevation from the elevation that would be expected at the equator, given the current date.

To measure longitude, determine the current time, using a sundial and a clock. Every 15° of longitude will introduce a discrepancy of one hour.

Prior to the invention of the marine chronometer by John Harrison in 1737, mariners estimated longitude, based on how long it took to make the trip. As you might imagine, this was not terribly accurate.

Actually, a chronometer is unnecessary. All you really need is a sundial, and a water clock. The ancient Greeks were already making very good ones. They were able to tell, for instance, when exactly twelve hours had elapsed.

Using a sundial, start your 12 hour water clock running at noon. At midnight, record the orientation of the stars. Henceforth, given the date, you can tell time at night, by observing the stars.

Now, we have two different methods for determining when midnight has arrived. We can use the sundial/water clock, or we can look at the stars. They should return the same answer, assuming we remain at the same location.

You can't use a water clock on a ship. But you can transport it, and set it up on another continent.

Determining when midnight has arrived, using the two methods already described, will now give us two different answers, with a discrepancy of one hour for every 15° of longitude.