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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
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