Or in the case of Antarctica…
Well, sure! First north, then south. 
Well, yes, but for each entity you’d choose an appropriate meridian for the zero point. Traditionally, this is done by choosing the meridian of the national observatory, usually located in the capital city of the entity.
For the British Empire, the standard longitude works because we happened to have chosen their meridian as the world standard. But to find the eastern and westernmost French possessions, you’d use the meridian of the Paris Observatory.
For the US, a meridian was established at the Naval Observatory in Washington DC. This meridian was used by Congress to set a number of north-south boundaries in the western states. Since it was (I think) about 7 minutes off the Greenwich system, those boundaries are now the same displacement from standard even degrees of longitude.
So to answer the question based on the Naval Observatory meridian, the easternmost point of the US is in Maine.
Uhh. Sorry. But that’s incorrect. If you start out going north and continue going in the same direction, you will go south after you pass the north pole. However, if you are planning to go north, you will do so as far as the north pole, and then you will just stop. You are now as north as you can get. Similarly for south.
dtilque; I accept your explaination. Please explain however why London is your capital, but Greenwich is used as the base line? The fact that any globe you buy in the U.S., France or Ethopia is going to use Greenwich as the base line also means that there are two ways of looking at the answer. However, someone that worries about which way he is moving as he crosses the IDL or someone that wants to stand facing across the line does not understand what this is all about.
Since I’m an American, London isn’t my capital, but I understand what you mean. (I guess my phrasing made it look like I was British.)
Greenwich is where the Royal Observatory is located, on a convenient spot on the River Thames. If you look at a map of London, you will find that it’s subdivided into a number of subregions (boroughs and the like). The one that’s called the City of London is a fairly small area in the center that’s primarily the financial district. Greenwich is an area downriver but it’s still part of Greater London.
The important thing about observatories was that they were the ones who figured out what time it was, a very important piece of data for calculating longitude. Every day at noon, the Royal Observatory would give a time signal visible to the ships anchored in the river and the ships would all set their clocks to that time. No doubt other major harbors had similar time signal services.
AFAIK, the Royal Greenwich Observatory is no longer used for astronomical purposes. I think it’s basically a museum now.
Throughout most of the 19th century, most countries had their own meridians but it was a potential source of confusion for navigators. For example, an American navigator using a British navigation chart would constantly be having to make adjustments to his figures.
So the major maritime nations got together in the 1880s to select a standard meridian for navigation purposes (I think this was also where they set up the time zones). The French, of course, couldn’t understand why anyone would not want their meridian, but they were outvoted and the British meridian was selected. No doubt the French are still crying foul.
Having the Greenwich-based longitudes on all kinds of maps means that people assume that that’s the only coordinates possible. I’m not sure what to tell them to convince them that there are times when Greenwich is not the most appropriate meridian to use.