quarter of an hour, to_ ISABEL, _who
comes up from under the table with her hair all about her ears, and the
last findable beads in her hand_). Mice are useful little things
sometimes. Now, mousie, I want all those beads crystallised. How many
ways are there of putting them in order?

ISABEL. Well, first one would string them, I suppose?

L. Yes, that's the first way. You cannot string ultimate atoms;
but you can put them in a row, and then they fasten themselves
together, somehow, into a long rod or needle. We will call these
'_Needle_-crystals.' What would be the next way?

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 endeavour_). 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 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 be