The air flows past unseen as one flies. As it flows the invisible meridians and parallels pass with it, sharp but arbitrary demarcations imposed mathematically by man upon a sphere which he learned to measure long after he began to move intelligently about its surface; geographically non-existent hair lines which stubble the ends of certain radii projecting to the surface from the centre of our globe. But these same lines are cartographically displayed upon our maps, where we designate them graticules. And so the air navigator, resolving his position in the air above the surface of the earth as a mathematically unique point, knows both cartographically and geographically exactly where he is.