all others, are too immediate and too vast to receive
correction from them. Besides, the very illusions of perspective are
needed to make us understand extension, and to help us in comparing its
parts. If there were no false appearances, we could see nothing at a
distance; if there were no gradations in size, we could form no
estimate of distance, or rather there would be no distance at all. If
of two trees the one a hundred paces away seemed as large and distinct
as the other, ten paces distant, we should place them side by side. If
we saw all objects in their true dimensions, we should see no space
whatever; everything would appear to be directly beneath our eye.

For judging of the size and distance of objects, sight has only one
measure, and that is the angle they form with our eye. As this is the
simple effect of a compound cause, the judgment we form from it leaves
each particular case undecided or is necessarily imperfect. For how
can I by the sight alone tell whether the angle which makes one object
appear smaller than another is caused by the really lesser magnitude of
the object or by its greater distance from me?

An opposite method must therefore be pursued. Instead of relying on
one sensation only, we must repeat it, verify it by others, subordinate
sight to touch, repressing the impetuosity of the first by the steady,
even pace of the second. For lack of this caution we measure very
inaccurately by the eye, in determining height, length, depth, and
distance. That this is not due to organic defect, but to careless use,
is proved by the fact that engineers, surveyors, architects, masons,
and painters generally have a far more accurate eye than we, and
estimate measures of extension more correctly. Their business gives
them experience that we neglect to acquire, and thus they correct the
ambiguity of the angle by means of appearances associated with it,
which enable them to determine more exactly the relation of the two
things producing the angle.

Children are easily led into anything that allows unconstrained
movement of the body. There are a thousand ways of interesting them in
measuring, discovering, and estimating distances. "Yonder is a very
tall cherry-tree; how can we manage to get some cherries? Will the
ladder in the barn do? There is a very wide brook; how can we cross
it? Would one of the planks in the yard be long enough? We want to
throw a line from our windows and catch some f