I will begin by sketching a man just as a boy would sketch one on a wall, with a dash 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.