"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? We're all out of a place again." And she sat down resignedly on a very low cricket, in the middle of the room. "I'll tell you what we'll do, mother," said Ruth, coming round. "I've thought of it this good while. We'll co-operate!" "She's glad of it! She's been waiting for a chance! I believe she put the luminary up to it! Ruth, you're a brick--moon!" CHAPTER VI. CO-OPERATING. When mother first read that article in the Atlantic she had said, right off,-- "I'm sure I wish they would!" "Would what, mother?" asked Barbara. "Co-operate." "O mother! I really do believe you must belong, somehow, to the Micawber family! I shouldn't wonder if one of these days, when they come into their luck, you should hear of something greatly to your advantage, from over the water. You have such faith in 'they'! I don't believe '_they_' will ever do much for '_us_'!" "What is it, dear?" asked Mrs. Hobart, rousing from a little arm-chair wink, during which Mrs. Holabird had taken up the magazine. Mrs. Hobart had come in, with her cable wool and her great ivory knitting-pins, to sit an hour, sociably. "Co-operative housekeeping, ma'am," said Barbara. "Oh! Yes. That is what they _used_ to have, in old times, when we lived at home with mother. Only they didn't write articles about it. All the women in a house co-operated--to keep it; and all the neighborhood co-operated--by living exactly in the same way. Nowadays, it's co-operative shirking; isn't it?" One never could quite tell whether Mrs. Hobart was more simple or sharp.