I am not well versed in the nautical mile navigation so forgive me if I get things wrong.
1. do they use the arbitrary distance or the long/lat lines as the guide as with the Gleason map which is also accurately used to navigate?
The circumference of the Earth....which the nautical mile is based on has it ever been confirmed/proven via measurement?
What you are asking about is the science of geodesy. As usual, Wikipedia gives an excellent introduction into the history and practise without getting too bogged down in detailed mathematical exactitude.



