Lily. Four rods of four beads each, I suppose.
L. Yes, and then five rods of five, and so on. But now, look here; make another square of four beads again. You see they leave a little opening in the centre.
Isabel (pushing two opposite ones closer together). Now they don't.
L. No; but now it isn't a square; and by pushing the two together you have pushed the two others farther apart.
Isabel. And yet, somehow, they all seem closer than they were!
L. Yes; for before, each of them only touched two of the others, but now each of the two in the middle touches the other three. Take away one of the outsiders, Isabel; now you have three in a triangle—the smallest triangle you can make out of the beads. Now put a rod of three beads on at one side. So, you have a triangle of six beads; but just the shape of the first one. Next a rod of four on the side of that; and you have a triangle of ten beads: then a rod of five on the side of that; and you have a triangle of fifteen. Thus you have a square with five beads on the side, and a triangle with five beads on the side; equal-sided, therefore, like the square. So, however few or many you may be, you may soon learn how to crystallise quickly into these two figures, which are the foundation of form in the commonest, and therefore actually the most important, as well as in the rarest, and therefore, by our esteem, the most important, minerals of the world. Look at this in my hand.
Violet. Why, it is leaf-gold!
L. Yes; but beaten by no man's hammer; or rather, not beaten at all, but woven. Besides, feel the weight of it. There is gold enough there to gild the walls and ceiling, if it were beaten thin.
Violet. How beautiful! And it glitters like a leaf covered with frost.
L. You only think it so beautiful because you know it is gold. It is not prettier, in reality, than a bit of brass: for it is Transylvanian gold; and they say there is a foolish gnome in the mines there, who is always wanting to live in the moon, and so alloys all the gold with a little silver. I don't know how that may be: but the silver always is in the gold; and if he does it, it's very provoking of him, for no gold is woven so fine anywhere else.