What is an east and west line?

To Chiles Terril on September 25, 1822:

On the question what is an east and west line? which, you say, has been a subject of discussion in the newspapers. I presume, however, it must have been a mere question of definition, and that the parties have differed only in applying the same appellation to different things. The one defines an east and west line to be on a great circle of the earth, passing through the point of departure, its nadir point, and the centre of the earth, its plane rectangular, to that of the meridian of departure. The other considers an east and west line to be a line on the surface of the earth, bounding a plane at right-angles with its axis, or a circle of latitude passing through the point of departure, or in other words, a line which, from the point of departure, passes every meridian at a right-angle. Each party, therefore, defining the line he means, may be permitted to call it an east and west one, or at least it becomes no longer a mathematical but a philological question of the meaning of the words east and west. The last is what was meant probably by the east and west line in the treaty of Ghent. The same has been the understanding in running the numerous east and west lines which divide our different States. They have been run by observations of latitude at very short intervals, uniting the points of observation by short direct lines, and thus constituting in fact part of a polygon of very short sides.