. He turns round, looks back and sees a black line sticking up from the earth at the point
, whence he started. The height of the line appears to him to have a certain magnitude; and in order to register this magnitude accurately, he measures with an instrument the precise visual angle under which he sees the black line. He then continues his journey, stops, turns round again and finds that the black line is now seen under a smaller visual angle, hence appears to him to be reduced in height. His first impulse would be to assume that the black line was due to some squirming mirage and, while a reality in so far as it affected his eyesight, yet could be endowed with no objective existence in any impersonal way. Yet, without even returning to the point
and investigating the matter more closely, our observer could soon find out that the black line must be produced by some existent entity. He would make this discovery in the following way: By combining the visual angle
under which the black line appeared to him with his distance
from the point