ISABEL. I suppose, as we are to get together in the playground, when it stops raining, in different shapes?
L. Yes; put the beads together, then, in the simplest form you can, to begin with. Put them into a square, and pack them close.
ISABEL (after careful endeavor). I can't get them closer.
L. That will do. Now you may see, beforehand, that if you try to throw yourselves into square in this confused way, you will never know your places; so you had better consider every square as made of rods, put side by side. Take four beads of equal size, first, Isabel; put them into a little square. That, you may consider as made up of two rods of two beads each. Then you can make a square a size larger, out of three rods of three. Then the next square may be a size larger. How many rods, Lily?
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 center.
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 crystallize 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.