had had private occupation.

"There had been family company at grandfather's," she told Jeannie
Hadden, one morning. "We had been very much engaged among ourselves.
We had hardly seen anything of the other girls for two or three
weeks."

Barbara sat at the round table, where Stephen had been doing his
geometry last night, twirling a pair of pencil compasses about on a
sheet of paper, while this was saying. She lifted up her eyes a
little, cornerwise, without moving her head, and gave a twinkle of
mischief over at mother and Ruth. When Jeannie was gone, she kept on
silently, a few minutes, with her diagrams. Then she said, in her
funniest, repressed way,--

"I can see a little how it must be; but I suppose I ought to
understand the differential calculus to compute it. Circles are
wonderful things; and the science of curves holds almost everything.
Rose, when do you think we shall get round again?"

She held up her bit of paper as she spoke, scrawled over with
intersecting circles and arcs and ellipses, against whose curves and
circumferences she had written names: Marchbanks, Hadden, Goldthwaite,
Holabird.

"It's a mere question of centre and radius," she said. "You may be big
enough to take in the whole of them, or you may only cut in at the
sides. You may be just tangent for a minute, and then go off into
space on your own account. You may have your centre barely inside of a
great ring, and yet reach pretty well out of it for a good part; you
_must_ be small to be taken quite in by anybody's!"

"It doesn't illustrate," said Rose, coolly. "Orbits don't snarl up in
that fashion."

"Geometry does," said Barbara. "I told you I couldn't work it all out.
But I suppose there's a Q.E.D. at the end of it somewhere."

* * * * *

Two or three days after something new happened; an old thing happened
freshly, rather,--which also had to do with our orbit and its
eccentricities. Barbara, as usual, discovered and announced it.

"I should think _any_ kind of an astronomer might be mad!" she
exclaimed. "Periods and distances are bad enough; but then come the
perturbations! Here's one. We're used to it, to be sure; but we never
know exactly where it may come in. The girl we live with has formed
other views for herself, and is going off at a tangent. What _is_ the
reason we can't keep a satellite,--planet, I mean?"

"Barbara!" said mother, anxiously, "don't be absurd!"

"Well, what shall I be