for each arm, and with fingers larger than the arms.
By and by one or the other of us will discover this disproportion. We
shall observe that a leg has thickness, and that this thickness is not
the same everywhere; that the length of the arm is determined by its
proportion to the body; and so on. As we go on I will do no more than
keep even step with him, or will excel him by so little that he can
always easily overtake and even surpass me. We will get colors and
brushes; we will try to imitate not only the outline but the coloring
and all the other details of objects. We will color; we will paint; we
will daub; but in all our daubing we shall be continually peering into
nature, and all we do shall be done under the eye of that great teacher.

If we had difficulty in finding decorations for our room, we have now
all we could desire. I will have our drawings framed, so that we can
give them no finishing touches; and this will make us both careful to
do no negligent work. I will arrange them in order around our room,
each drawing repeated twenty or thirty times, and each repetition
showing the author's progress, from the representation of a house by an
almost shapeless attempt at a square, to the accurate copy of its front
elevation, profile, proportions, and shading. The drawings thus graded
must be interesting to ourselves, curious to others, and likely to
stimulate further effort. I will inclose the first and rudest of these
in showy gilded frames, to set them off well; but as the imitation
improves, and when the drawing is really good, I will add only a very
simple black frame. The picture needs no ornament but itself, and it
would be a pity that the bordering should receive half the attention.

Both of us will aspire to the honor of a plain frame, and if either
wishes to condemn the other's drawing, he will say it ought to have a
gilt frame. Perhaps some day these gilded frames will pass into a
proverb with us, and we shall be interested to observe how many men do
justice to themselves by framing themselves in the very same way.

Geometry.

I have said that geometry is not intelligible to children; but it is
our own fault. We do not observe that their method is different from
ours, and that what is to us the art of reasoning should be to them
only the art of seeing. Instead of giving them our method, we should
do better to take theirs. For in our way of learning geometry,
imagination really does as