All Mariners.........In Great Circle Navigation, why is it that yr Rhumbline Course will end at the poles..?

Answer 1

A rhumbline course crosses each meridian of longitude at the same angle. If you get a globe, you'll see that provided this angle isn't 90 degrees, in which case your course would be a line of latitude, you'll either be going straight up a meridian to the pole, or you'll be spiralling towards a pole.